---
_id: '63247'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. A switch in dimension dependence of critical blow-up exponents
    in a Keller-Segel system involving indirect signal production. <i>Journal of Differential
    Equations</i>. 2025;423:197-239. doi:<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>
  apa: Tao, Y., &#38; Winkler, M. (2025). A switch in dimension dependence of critical
    blow-up exponents in a Keller-Segel system involving indirect signal production.
    <i>Journal of Differential Equations</i>, <i>423</i>, 197–239. <a href="https://doi.org/10.1016/j.jde.2024.12.040">https://doi.org/10.1016/j.jde.2024.12.040</a>
  bibtex: '@article{Tao_Winkler_2025, title={A switch in dimension dependence of critical
    blow-up exponents in a Keller-Segel system involving indirect signal production},
    volume={423}, DOI={<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao,
    Youshan and Winkler, Michael}, year={2025}, pages={197–239} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “A Switch in Dimension Dependence of
    Critical Blow-up Exponents in a Keller-Segel System Involving Indirect Signal
    Production.” <i>Journal of Differential Equations</i> 423 (2025): 197–239. <a
    href="https://doi.org/10.1016/j.jde.2024.12.040">https://doi.org/10.1016/j.jde.2024.12.040</a>.'
  ieee: 'Y. Tao and M. Winkler, “A switch in dimension dependence of critical blow-up
    exponents in a Keller-Segel system involving indirect signal production,” <i>Journal
    of Differential Equations</i>, vol. 423, pp. 197–239, 2025, doi: <a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>.'
  mla: Tao, Youshan, and Michael Winkler. “A Switch in Dimension Dependence of Critical
    Blow-up Exponents in a Keller-Segel System Involving Indirect Signal Production.”
    <i>Journal of Differential Equations</i>, vol. 423, Elsevier BV, 2025, pp. 197–239,
    doi:<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 423 (2025) 197–239.
date_created: 2025-12-18T19:01:40Z
date_updated: 2025-12-18T20:12:58Z
doi: 10.1016/j.jde.2024.12.040
intvolume: '       423'
language:
- iso: eng
page: 197-239
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: A switch in dimension dependence of critical blow-up exponents in a Keller-Segel
  system involving indirect signal production
type: journal_article
user_id: '31496'
volume: 423
year: '2025'
...
---
_id: '60205'
article_number: '113555'
author:
- first_name: Tobias
  full_name: Black, Tobias
  id: '23686'
  last_name: Black
  orcid: 0000-0001-9963-0800
citation:
  ama: 'Black T. Very mild diffusion enhancement and singular sensitivity: Existence
    of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system.
    <i>Journal of Differential Equations</i>. 2025;443. doi:<a href="https://doi.org/10.1016/j.jde.2025.113555">10.1016/j.jde.2025.113555</a>'
  apa: 'Black, T. (2025). Very mild diffusion enhancement and singular sensitivity:
    Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes
    system. <i>Journal of Differential Equations</i>, <i>443</i>, Article 113555.
    <a href="https://doi.org/10.1016/j.jde.2025.113555">https://doi.org/10.1016/j.jde.2025.113555</a>'
  bibtex: '@article{Black_2025, title={Very mild diffusion enhancement and singular
    sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes
    system}, volume={443}, DOI={<a href="https://doi.org/10.1016/j.jde.2025.113555">10.1016/j.jde.2025.113555</a>},
    number={113555}, journal={Journal of Differential Equations}, publisher={Elsevier
    BV}, author={Black, Tobias}, year={2025} }'
  chicago: 'Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity:
    Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes
    System.” <i>Journal of Differential Equations</i> 443 (2025). <a href="https://doi.org/10.1016/j.jde.2025.113555">https://doi.org/10.1016/j.jde.2025.113555</a>.'
  ieee: 'T. Black, “Very mild diffusion enhancement and singular sensitivity: Existence
    of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system,”
    <i>Journal of Differential Equations</i>, vol. 443, Art. no. 113555, 2025, doi:
    <a href="https://doi.org/10.1016/j.jde.2025.113555">10.1016/j.jde.2025.113555</a>.'
  mla: 'Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity:
    Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes
    System.” <i>Journal of Differential Equations</i>, vol. 443, 113555, Elsevier
    BV, 2025, doi:<a href="https://doi.org/10.1016/j.jde.2025.113555">10.1016/j.jde.2025.113555</a>.'
  short: T. Black, Journal of Differential Equations 443 (2025).
date_created: 2025-06-13T11:12:23Z
date_updated: 2025-06-13T11:13:22Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1016/j.jde.2025.113555
intvolume: '       443'
language:
- iso: eng
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: 'Very mild diffusion enhancement and singular sensitivity: Existence of bounded
  weak solutions in a two-dimensional chemotaxis-Navier–Stokes system'
type: journal_article
user_id: '23686'
volume: 443
year: '2025'
...
---
_id: '63263'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. L∞ bounds in a two-dimensional doubly degenerate nutrient taxis
    system with general cross-diffusive flux. <i>Journal of Differential Equations</i>.
    2024;400:423-456. doi:<a href="https://doi.org/10.1016/j.jde.2024.04.028">10.1016/j.jde.2024.04.028</a>
  apa: Winkler, M. (2024). L∞ bounds in a two-dimensional doubly degenerate nutrient
    taxis system with general cross-diffusive flux. <i>Journal of Differential Equations</i>,
    <i>400</i>, 423–456. <a href="https://doi.org/10.1016/j.jde.2024.04.028">https://doi.org/10.1016/j.jde.2024.04.028</a>
  bibtex: '@article{Winkler_2024, title={L∞ bounds in a two-dimensional doubly degenerate
    nutrient taxis system with general cross-diffusive flux}, volume={400}, DOI={<a
    href="https://doi.org/10.1016/j.jde.2024.04.028">10.1016/j.jde.2024.04.028</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler,
    Michael}, year={2024}, pages={423–456} }'
  chicago: 'Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient
    Taxis System with General Cross-Diffusive Flux.” <i>Journal of Differential Equations</i>
    400 (2024): 423–56. <a href="https://doi.org/10.1016/j.jde.2024.04.028">https://doi.org/10.1016/j.jde.2024.04.028</a>.'
  ieee: 'M. Winkler, “L∞ bounds in a two-dimensional doubly degenerate nutrient taxis
    system with general cross-diffusive flux,” <i>Journal of Differential Equations</i>,
    vol. 400, pp. 423–456, 2024, doi: <a href="https://doi.org/10.1016/j.jde.2024.04.028">10.1016/j.jde.2024.04.028</a>.'
  mla: Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient
    Taxis System with General Cross-Diffusive Flux.” <i>Journal of Differential Equations</i>,
    vol. 400, Elsevier BV, 2024, pp. 423–56, doi:<a href="https://doi.org/10.1016/j.jde.2024.04.028">10.1016/j.jde.2024.04.028</a>.
  short: M. Winkler, Journal of Differential Equations 400 (2024) 423–456.
date_created: 2025-12-18T19:09:07Z
date_updated: 2025-12-18T20:15:05Z
doi: 10.1016/j.jde.2024.04.028
intvolume: '       400'
language:
- iso: eng
page: 423-456
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with
  general cross-diffusive flux
type: journal_article
user_id: '31496'
volume: 400
year: '2024'
...
---
_id: '34793'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Glöckner H, Hilgert J. Aspects of control theory on infinite-dimensional Lie
    groups and G-manifolds. <i>Journal of Differential Equations</i>. 2023;343:186–232.
    doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>
  apa: Glöckner, H., &#38; Hilgert, J. (2023). Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds. <i>Journal of Differential Equations</i>, <i>343</i>,
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>
  bibtex: '@article{Glöckner_Hilgert_2023, title={Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>},
    journal={Journal of Differential Equations}, author={Glöckner, Helge and Hilgert,
    Joachim}, year={2023}, pages={186–232} }'
  chicago: 'Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i> 343 (2023):
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>.'
  ieee: 'H. Glöckner and J. Hilgert, “Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds,” <i>Journal of Differential Equations</i>, vol. 343,
    pp. 186–232, 2023, doi: <a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.'
  mla: Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i>, vol. 343,
    2023, pp. 186–232, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.
  short: H. Glöckner, J. Hilgert, Journal of Differential Equations 343 (2023) 186–232.
date_created: 2022-12-21T19:31:13Z
date_updated: 2024-03-22T16:02:32Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
- _id: '91'
doi: 10.1016/j.jde.2022.10.001
external_id:
  arxiv:
  - '2007.11277'
intvolume: '       343'
keyword:
- '22E65'
- 28B05
- 34A12
- 34H05
- '46E30'
- '46E40'
language:
- iso: eng
page: 186–232
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
quality_controlled: '1'
status: public
title: Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
type: journal_article
user_id: '178'
volume: 343
year: '2023'
...
---
_id: '53342'
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
- first_name: Tomomi
  full_name: Yokota, Tomomi
  last_name: Yokota
citation:
  ama: Winkler M, Yokota T. Avoiding critical mass phenomena by arbitrarily mild saturation
    of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems.
    <i>Journal of Differential Equations</i>. 2023;374:1-28. doi:<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>
  apa: Winkler, M., &#38; Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily
    mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems. <i>Journal of Differential Equations</i>, <i>374</i>, 1–28. <a href="https://doi.org/10.1016/j.jde.2023.07.029">https://doi.org/10.1016/j.jde.2023.07.029</a>
  bibtex: '@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by
    arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems}, volume={374}, DOI={<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler,
    Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }'
  chicago: 'Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena
    by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes
    Systems.” <i>Journal of Differential Equations</i> 374 (2023): 1–28. <a href="https://doi.org/10.1016/j.jde.2023.07.029">https://doi.org/10.1016/j.jde.2023.07.029</a>.'
  ieee: 'M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily
    mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems,” <i>Journal of Differential Equations</i>, vol. 374, pp. 1–28, 2023,
    doi: <a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>.'
  mla: Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily
    Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes
    Systems.” <i>Journal of Differential Equations</i>, vol. 374, Elsevier BV, 2023,
    pp. 1–28, doi:<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>.
  short: M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.
date_created: 2024-04-07T12:53:32Z
date_updated: 2024-04-07T12:53:38Z
doi: 10.1016/j.jde.2023.07.029
intvolume: '       374'
keyword:
- Analysis
- Applied Mathematics
language:
- iso: eng
page: 1-28
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive
  fluxes in two-dimensional Keller-Segel-Navier-Stokes systems
type: journal_article
user_id: '31496'
volume: 374
year: '2023'
...
---
_id: '63289'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
- first_name: Tomomi
  full_name: Yokota, Tomomi
  last_name: Yokota
citation:
  ama: Winkler M, Yokota T. Avoiding critical mass phenomena by arbitrarily mild saturation
    of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems.
    <i>Journal of Differential Equations</i>. 2023;374:1-28. doi:<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>
  apa: Winkler, M., &#38; Yokota, T. (2023). Avoiding critical mass phenomena by arbitrarily
    mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems. <i>Journal of Differential Equations</i>, <i>374</i>, 1–28. <a href="https://doi.org/10.1016/j.jde.2023.07.029">https://doi.org/10.1016/j.jde.2023.07.029</a>
  bibtex: '@article{Winkler_Yokota_2023, title={Avoiding critical mass phenomena by
    arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems}, volume={374}, DOI={<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler,
    Michael and Yokota, Tomomi}, year={2023}, pages={1–28} }'
  chicago: 'Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena
    by Arbitrarily Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes
    Systems.” <i>Journal of Differential Equations</i> 374 (2023): 1–28. <a href="https://doi.org/10.1016/j.jde.2023.07.029">https://doi.org/10.1016/j.jde.2023.07.029</a>.'
  ieee: 'M. Winkler and T. Yokota, “Avoiding critical mass phenomena by arbitrarily
    mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes
    systems,” <i>Journal of Differential Equations</i>, vol. 374, pp. 1–28, 2023,
    doi: <a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>.'
  mla: Winkler, Michael, and Tomomi Yokota. “Avoiding Critical Mass Phenomena by Arbitrarily
    Mild Saturation of Cross-Diffusive Fluxes in Two-Dimensional Keller-Segel-Navier-Stokes
    Systems.” <i>Journal of Differential Equations</i>, vol. 374, Elsevier BV, 2023,
    pp. 1–28, doi:<a href="https://doi.org/10.1016/j.jde.2023.07.029">10.1016/j.jde.2023.07.029</a>.
  short: M. Winkler, T. Yokota, Journal of Differential Equations 374 (2023) 1–28.
date_created: 2025-12-18T19:19:57Z
date_updated: 2025-12-18T20:07:42Z
doi: 10.1016/j.jde.2023.07.029
intvolume: '       374'
language:
- iso: eng
page: 1-28
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive
  fluxes in two-dimensional Keller-Segel-Navier-Stokes systems
type: journal_article
user_id: '31496'
volume: 374
year: '2023'
...
---
_id: '53327'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving
    singularly signal-dependent motilities in domains of arbitrary dimension. <i>Journal
    of Differential Equations</i>. 2022;343:390-418. doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>
  apa: Tao, Y., &#38; Winkler, M. (2022). Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension. <i>Journal of Differential Equations</i>, <i>343</i>, 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>
  bibtex: '@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao,
    Youshan and Winkler, Michael}, year={2022}, pages={390–418} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i> 343 (2022): 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system
    involving singularly signal-dependent motilities in domains of arbitrary dimension,”
    <i>Journal of Differential Equations</i>, vol. 343, pp. 390–418, 2022, doi: <a
    href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i>, vol. 343, Elsevier BV, 2022,
    pp. 390–418, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418.
date_created: 2024-04-07T12:42:28Z
date_updated: 2024-04-07T12:42:32Z
doi: 10.1016/j.jde.2022.10.022
intvolume: '       343'
keyword:
- Analysis
- Applied Mathematics
language:
- iso: eng
page: 390-418
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global solutions to a Keller-Segel-consumption system involving singularly
  signal-dependent motilities in domains of arbitrary dimension
type: journal_article
user_id: '31496'
volume: 343
year: '2022'
...
---
_id: '63272'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving
    singularly signal-dependent motilities in domains of arbitrary dimension. <i>Journal
    of Differential Equations</i>. 2022;343:390-418. doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>
  apa: Tao, Y., &#38; Winkler, M. (2022). Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension. <i>Journal of Differential Equations</i>, <i>343</i>, 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>
  bibtex: '@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao,
    Youshan and Winkler, Michael}, year={2022}, pages={390–418} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i> 343 (2022): 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system
    involving singularly signal-dependent motilities in domains of arbitrary dimension,”
    <i>Journal of Differential Equations</i>, vol. 343, pp. 390–418, 2022, doi: <a
    href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i>, vol. 343, Elsevier BV, 2022,
    pp. 390–418, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418.
date_created: 2025-12-18T19:13:04Z
date_updated: 2025-12-18T20:11:02Z
doi: 10.1016/j.jde.2022.10.022
intvolume: '       343'
language:
- iso: eng
page: 390-418
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global solutions to a Keller-Segel-consumption system involving singularly
  signal-dependent motilities in domains of arbitrary dimension
type: journal_article
user_id: '31496'
volume: 343
year: '2022'
...
---
_id: '63307'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Unlimited growth in logarithmic Keller-Segel systems. <i>Journal
    of Differential Equations</i>. 2021;309:74-97. doi:<a href="https://doi.org/10.1016/j.jde.2021.11.026">10.1016/j.jde.2021.11.026</a>
  apa: Winkler, M. (2021). Unlimited growth in logarithmic Keller-Segel systems. <i>Journal
    of Differential Equations</i>, <i>309</i>, 74–97. <a href="https://doi.org/10.1016/j.jde.2021.11.026">https://doi.org/10.1016/j.jde.2021.11.026</a>
  bibtex: '@article{Winkler_2021, title={Unlimited growth in logarithmic Keller-Segel
    systems}, volume={309}, DOI={<a href="https://doi.org/10.1016/j.jde.2021.11.026">10.1016/j.jde.2021.11.026</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler,
    Michael}, year={2021}, pages={74–97} }'
  chicago: 'Winkler, Michael. “Unlimited Growth in Logarithmic Keller-Segel Systems.”
    <i>Journal of Differential Equations</i> 309 (2021): 74–97. <a href="https://doi.org/10.1016/j.jde.2021.11.026">https://doi.org/10.1016/j.jde.2021.11.026</a>.'
  ieee: 'M. Winkler, “Unlimited growth in logarithmic Keller-Segel systems,” <i>Journal
    of Differential Equations</i>, vol. 309, pp. 74–97, 2021, doi: <a href="https://doi.org/10.1016/j.jde.2021.11.026">10.1016/j.jde.2021.11.026</a>.'
  mla: Winkler, Michael. “Unlimited Growth in Logarithmic Keller-Segel Systems.” <i>Journal
    of Differential Equations</i>, vol. 309, Elsevier BV, 2021, pp. 74–97, doi:<a
    href="https://doi.org/10.1016/j.jde.2021.11.026">10.1016/j.jde.2021.11.026</a>.
  short: M. Winkler, Journal of Differential Equations 309 (2021) 74–97.
date_created: 2025-12-18T19:27:16Z
date_updated: 2025-12-18T20:05:02Z
doi: 10.1016/j.jde.2021.11.026
intvolume: '       309'
language:
- iso: eng
page: 74-97
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Unlimited growth in logarithmic Keller-Segel systems
type: journal_article
user_id: '31496'
volume: 309
year: '2021'
...
---
_id: '63334'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global classical solutions to a doubly haptotactic cross-diffusion
    system modeling oncolytic virotherapy. <i>Journal of Differential Equations</i>.
    2019;268(9):4973-4997. doi:<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Global classical solutions to a doubly haptotactic
    cross-diffusion system modeling oncolytic virotherapy. <i>Journal of Differential
    Equations</i>, <i>268</i>(9), 4973–4997. <a href="https://doi.org/10.1016/j.jde.2019.10.046">https://doi.org/10.1016/j.jde.2019.10.046</a>
  bibtex: '@article{Tao_Winkler_2019, title={Global classical solutions to a doubly
    haptotactic cross-diffusion system modeling oncolytic virotherapy}, volume={268},
    DOI={<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>},
    number={9}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Tao, Youshan and Winkler, Michael}, year={2019}, pages={4973–4997} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Classical Solutions to a Doubly
    Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy.” <i>Journal
    of Differential Equations</i> 268, no. 9 (2019): 4973–97. <a href="https://doi.org/10.1016/j.jde.2019.10.046">https://doi.org/10.1016/j.jde.2019.10.046</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global classical solutions to a doubly haptotactic
    cross-diffusion system modeling oncolytic virotherapy,” <i>Journal of Differential
    Equations</i>, vol. 268, no. 9, pp. 4973–4997, 2019, doi: <a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Classical Solutions to a Doubly
    Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy.” <i>Journal
    of Differential Equations</i>, vol. 268, no. 9, Elsevier BV, 2019, pp. 4973–97,
    doi:<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 268 (2019) 4973–4997.
date_created: 2025-12-18T19:40:07Z
date_updated: 2025-12-18T20:01:29Z
doi: 10.1016/j.jde.2019.10.046
intvolume: '       268'
issue: '9'
language:
- iso: eng
page: 4973-4997
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global classical solutions to a doubly haptotactic cross-diffusion system modeling
  oncolytic virotherapy
type: journal_article
user_id: '31496'
volume: 268
year: '2019'
...
---
_id: '63357'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global smooth solvability of a parabolic–elliptic nutrient
    taxis system in domains of arbitrary dimension. <i>Journal of Differential Equations</i>.
    2019;267(1):388-406. doi:<a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension. <i>Journal of Differential
    Equations</i>, <i>267</i>(1), 388–406. <a href="https://doi.org/10.1016/j.jde.2019.01.014">https://doi.org/10.1016/j.jde.2019.01.014</a>
  bibtex: '@article{Tao_Winkler_2019, title={Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension}, volume={267}, DOI={<a
    href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>},
    number={1}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Tao, Youshan and Winkler, Michael}, year={2019}, pages={388–406} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solvability of a Parabolic–Elliptic
    Nutrient Taxis System in Domains of Arbitrary Dimension.” <i>Journal of Differential
    Equations</i> 267, no. 1 (2019): 388–406. <a href="https://doi.org/10.1016/j.jde.2019.01.014">https://doi.org/10.1016/j.jde.2019.01.014</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension,” <i>Journal of Differential
    Equations</i>, vol. 267, no. 1, pp. 388–406, 2019, doi: <a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solvability of a Parabolic–Elliptic
    Nutrient Taxis System in Domains of Arbitrary Dimension.” <i>Journal of Differential
    Equations</i>, vol. 267, no. 1, Elsevier BV, 2019, pp. 388–406, doi:<a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 267 (2019) 388–406.
date_created: 2025-12-19T10:55:53Z
date_updated: 2025-12-19T10:56:01Z
doi: 10.1016/j.jde.2019.01.014
intvolume: '       267'
issue: '1'
language:
- iso: eng
page: 388-406
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global smooth solvability of a parabolic–elliptic nutrient taxis system in
  domains of arbitrary dimension
type: journal_article
user_id: '31496'
volume: 267
year: '2019'
...
---
_id: '34666'
author:
- first_name: Tobias
  full_name: Black, Tobias
  id: '23686'
  last_name: Black
  orcid: 0000-0001-9963-0800
citation:
  ama: Black T. Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes
    system in 2D. <i>Journal of Differential Equations</i>. 2018;265(5):2296-2339.
    doi:<a href="https://doi.org/10.1016/j.jde.2018.04.035">10.1016/j.jde.2018.04.035</a>
  apa: Black, T. (2018). Eventual smoothness of generalized solutions to a singular
    chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>, <i>265</i>(5),
    2296–2339. <a href="https://doi.org/10.1016/j.jde.2018.04.035">https://doi.org/10.1016/j.jde.2018.04.035</a>
  bibtex: '@article{Black_2018, title={Eventual smoothness of generalized solutions
    to a singular chemotaxis-Stokes system in 2D}, volume={265}, DOI={<a href="https://doi.org/10.1016/j.jde.2018.04.035">10.1016/j.jde.2018.04.035</a>},
    number={5}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Black, Tobias}, year={2018}, pages={2296–2339} }'
  chicago: 'Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular
    Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i> 265,
    no. 5 (2018): 2296–2339. <a href="https://doi.org/10.1016/j.jde.2018.04.035">https://doi.org/10.1016/j.jde.2018.04.035</a>.'
  ieee: 'T. Black, “Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes
    system in 2D,” <i>Journal of Differential Equations</i>, vol. 265, no. 5, pp.
    2296–2339, 2018, doi: <a href="https://doi.org/10.1016/j.jde.2018.04.035">10.1016/j.jde.2018.04.035</a>.'
  mla: Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular
    Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i>, vol.
    265, no. 5, Elsevier BV, 2018, pp. 2296–339, doi:<a href="https://doi.org/10.1016/j.jde.2018.04.035">10.1016/j.jde.2018.04.035</a>.
  short: T. Black, Journal of Differential Equations 265 (2018) 2296–2339.
date_created: 2022-12-21T09:47:19Z
date_updated: 2022-12-21T10:05:11Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1016/j.jde.2018.04.035
intvolume: '       265'
issue: '5'
keyword:
- Analysis
- Applied Mathematics
language:
- iso: eng
page: 2296-2339
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes
  system in 2D
type: journal_article
user_id: '23686'
volume: 265
year: '2018'
...
---
_id: '63365'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Global classical solvability and generic infinite-time blow-up in
    quasilinear Keller–Segel systems with bounded sensitivities. <i>Journal of Differential
    Equations</i>. 2018;266(12):8034-8066. doi:<a href="https://doi.org/10.1016/j.jde.2018.12.019">10.1016/j.jde.2018.12.019</a>
  apa: Winkler, M. (2018). Global classical solvability and generic infinite-time
    blow-up in quasilinear Keller–Segel systems with bounded sensitivities. <i>Journal
    of Differential Equations</i>, <i>266</i>(12), 8034–8066. <a href="https://doi.org/10.1016/j.jde.2018.12.019">https://doi.org/10.1016/j.jde.2018.12.019</a>
  bibtex: '@article{Winkler_2018, title={Global classical solvability and generic
    infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities},
    volume={266}, DOI={<a href="https://doi.org/10.1016/j.jde.2018.12.019">10.1016/j.jde.2018.12.019</a>},
    number={12}, journal={Journal of Differential Equations}, publisher={Elsevier
    BV}, author={Winkler, Michael}, year={2018}, pages={8034–8066} }'
  chicago: 'Winkler, Michael. “Global Classical Solvability and Generic Infinite-Time
    Blow-up in Quasilinear Keller–Segel Systems with Bounded Sensitivities.” <i>Journal
    of Differential Equations</i> 266, no. 12 (2018): 8034–66. <a href="https://doi.org/10.1016/j.jde.2018.12.019">https://doi.org/10.1016/j.jde.2018.12.019</a>.'
  ieee: 'M. Winkler, “Global classical solvability and generic infinite-time blow-up
    in quasilinear Keller–Segel systems with bounded sensitivities,” <i>Journal of
    Differential Equations</i>, vol. 266, no. 12, pp. 8034–8066, 2018, doi: <a href="https://doi.org/10.1016/j.jde.2018.12.019">10.1016/j.jde.2018.12.019</a>.'
  mla: Winkler, Michael. “Global Classical Solvability and Generic Infinite-Time Blow-up
    in Quasilinear Keller–Segel Systems with Bounded Sensitivities.” <i>Journal of
    Differential Equations</i>, vol. 266, no. 12, Elsevier BV, 2018, pp. 8034–66,
    doi:<a href="https://doi.org/10.1016/j.jde.2018.12.019">10.1016/j.jde.2018.12.019</a>.
  short: M. Winkler, Journal of Differential Equations 266 (2018) 8034–8066.
date_created: 2025-12-19T11:00:24Z
date_updated: 2025-12-19T11:00:31Z
doi: 10.1016/j.jde.2018.12.019
intvolume: '       266'
issue: '12'
language:
- iso: eng
page: 8034-8066
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global classical solvability and generic infinite-time blow-up in quasilinear
  Keller–Segel systems with bounded sensitivities
type: journal_article
user_id: '31496'
volume: 266
year: '2018'
...
---
_id: '63380'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Global existence and stabilization in a degenerate chemotaxis-Stokes
    system with mildly strong diffusion enhancement. <i>Journal of Differential Equations</i>.
    2018;264(10):6109-6151. doi:<a href="https://doi.org/10.1016/j.jde.2018.01.027">10.1016/j.jde.2018.01.027</a>
  apa: Winkler, M. (2018). Global existence and stabilization in a degenerate chemotaxis-Stokes
    system with mildly strong diffusion enhancement. <i>Journal of Differential Equations</i>,
    <i>264</i>(10), 6109–6151. <a href="https://doi.org/10.1016/j.jde.2018.01.027">https://doi.org/10.1016/j.jde.2018.01.027</a>
  bibtex: '@article{Winkler_2018, title={Global existence and stabilization in a degenerate
    chemotaxis-Stokes system with mildly strong diffusion enhancement}, volume={264},
    DOI={<a href="https://doi.org/10.1016/j.jde.2018.01.027">10.1016/j.jde.2018.01.027</a>},
    number={10}, journal={Journal of Differential Equations}, publisher={Elsevier
    BV}, author={Winkler, Michael}, year={2018}, pages={6109–6151} }'
  chicago: 'Winkler, Michael. “Global Existence and Stabilization in a Degenerate
    Chemotaxis-Stokes System with Mildly Strong Diffusion Enhancement.” <i>Journal
    of Differential Equations</i> 264, no. 10 (2018): 6109–51. <a href="https://doi.org/10.1016/j.jde.2018.01.027">https://doi.org/10.1016/j.jde.2018.01.027</a>.'
  ieee: 'M. Winkler, “Global existence and stabilization in a degenerate chemotaxis-Stokes
    system with mildly strong diffusion enhancement,” <i>Journal of Differential Equations</i>,
    vol. 264, no. 10, pp. 6109–6151, 2018, doi: <a href="https://doi.org/10.1016/j.jde.2018.01.027">10.1016/j.jde.2018.01.027</a>.'
  mla: Winkler, Michael. “Global Existence and Stabilization in a Degenerate Chemotaxis-Stokes
    System with Mildly Strong Diffusion Enhancement.” <i>Journal of Differential Equations</i>,
    vol. 264, no. 10, Elsevier BV, 2018, pp. 6109–51, doi:<a href="https://doi.org/10.1016/j.jde.2018.01.027">10.1016/j.jde.2018.01.027</a>.
  short: M. Winkler, Journal of Differential Equations 264 (2018) 6109–6151.
date_created: 2025-12-19T11:08:16Z
date_updated: 2025-12-19T11:08:22Z
doi: 10.1016/j.jde.2018.01.027
intvolume: '       264'
issue: '10'
language:
- iso: eng
page: 6109-6151
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global existence and stabilization in a degenerate chemotaxis-Stokes system
  with mildly strong diffusion enhancement
type: journal_article
user_id: '31496'
volume: 264
year: '2018'
...
---
_id: '63379'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Renormalized radial large-data solutions to the higher-dimensional
    Keller–Segel system with singular sensitivity and signal absorption. <i>Journal
    of Differential Equations</i>. 2017;264(3):2310-2350. doi:<a href="https://doi.org/10.1016/j.jde.2017.10.029">10.1016/j.jde.2017.10.029</a>
  apa: Winkler, M. (2017). Renormalized radial large-data solutions to the higher-dimensional
    Keller–Segel system with singular sensitivity and signal absorption. <i>Journal
    of Differential Equations</i>, <i>264</i>(3), 2310–2350. <a href="https://doi.org/10.1016/j.jde.2017.10.029">https://doi.org/10.1016/j.jde.2017.10.029</a>
  bibtex: '@article{Winkler_2017, title={Renormalized radial large-data solutions
    to the higher-dimensional Keller–Segel system with singular sensitivity and signal
    absorption}, volume={264}, DOI={<a href="https://doi.org/10.1016/j.jde.2017.10.029">10.1016/j.jde.2017.10.029</a>},
    number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Winkler, Michael}, year={2017}, pages={2310–2350} }'
  chicago: 'Winkler, Michael. “Renormalized Radial Large-Data Solutions to the Higher-Dimensional
    Keller–Segel System with Singular Sensitivity and Signal Absorption.” <i>Journal
    of Differential Equations</i> 264, no. 3 (2017): 2310–50. <a href="https://doi.org/10.1016/j.jde.2017.10.029">https://doi.org/10.1016/j.jde.2017.10.029</a>.'
  ieee: 'M. Winkler, “Renormalized radial large-data solutions to the higher-dimensional
    Keller–Segel system with singular sensitivity and signal absorption,” <i>Journal
    of Differential Equations</i>, vol. 264, no. 3, pp. 2310–2350, 2017, doi: <a href="https://doi.org/10.1016/j.jde.2017.10.029">10.1016/j.jde.2017.10.029</a>.'
  mla: Winkler, Michael. “Renormalized Radial Large-Data Solutions to the Higher-Dimensional
    Keller–Segel System with Singular Sensitivity and Signal Absorption.” <i>Journal
    of Differential Equations</i>, vol. 264, no. 3, Elsevier BV, 2017, pp. 2310–50,
    doi:<a href="https://doi.org/10.1016/j.jde.2017.10.029">10.1016/j.jde.2017.10.029</a>.
  short: M. Winkler, Journal of Differential Equations 264 (2017) 2310–2350.
date_created: 2025-12-19T11:07:52Z
date_updated: 2025-12-19T11:07:59Z
doi: 10.1016/j.jde.2017.10.029
intvolume: '       264'
issue: '3'
language:
- iso: eng
page: 2310-2350
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Renormalized radial large-data solutions to the higher-dimensional Keller–Segel
  system with singular sensitivity and signal absorption
type: journal_article
user_id: '31496'
volume: 264
year: '2017'
...