---
_id: '63243'
article_number: '286'
author:
- first_name: Francesca
  full_name: Colasuonno, Francesca
  last_name: Colasuonno
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Colasuonno F, Winkler M. Stability vs.~instability of singular steady states
    in the parabolic-elliptic Keller-Segel system on $\R^n$. <i>ANNALI SCUOLA NORMALE
    SUPERIORE - CLASSE DI SCIENZE</i>. Published online 2023. doi:<a href="https://doi.org/10.2422/2036-2145.202303_006">10.2422/2036-2145.202303_006</a>
  apa: Colasuonno, F., &#38; Winkler, M. (2023). Stability vs.~instability of singular
    steady states in the parabolic-elliptic Keller-Segel system on $\R^n$. <i>ANNALI
    SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Article 286. <a href="https://doi.org/10.2422/2036-2145.202303_006">https://doi.org/10.2422/2036-2145.202303_006</a>
  bibtex: '@article{Colasuonno_Winkler_2023, title={Stability vs.~instability of singular
    steady states in the parabolic-elliptic Keller-Segel system on $\R^n$}, DOI={<a
    href="https://doi.org/10.2422/2036-2145.202303_006">10.2422/2036-2145.202303_006</a>},
    number={286}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola
    Normale Superiore - Edizioni della Normale}, author={Colasuonno, Francesca and
    Winkler, Michael}, year={2023} }'
  chicago: Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability
    of Singular Steady States in the Parabolic-Elliptic Keller-Segel System on $\R^n$.”
    <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, 2023. <a href="https://doi.org/10.2422/2036-2145.202303_006">https://doi.org/10.2422/2036-2145.202303_006</a>.
  ieee: 'F. Colasuonno and M. Winkler, “Stability vs.~instability of singular steady
    states in the parabolic-elliptic Keller-Segel system on $\R^n$,” <i>ANNALI SCUOLA
    NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Art. no. 286, 2023, doi: <a href="https://doi.org/10.2422/2036-2145.202303_006">10.2422/2036-2145.202303_006</a>.'
  mla: Colasuonno, Francesca, and Michael Winkler. “Stability vs.~instability of Singular
    Steady States in the Parabolic-Elliptic Keller-Segel System on $\R^n$.” <i>ANNALI
    SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, 286, Scuola Normale Superiore
    - Edizioni della Normale, 2023, doi:<a href="https://doi.org/10.2422/2036-2145.202303_006">10.2422/2036-2145.202303_006</a>.
  short: F. Colasuonno, M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
    (2023).
date_created: 2025-12-18T18:58:40Z
date_updated: 2025-12-18T20:17:21Z
doi: 10.2422/2036-2145.202303_006
language:
- iso: eng
publication: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
publication_identifier:
  issn:
  - 2036-2145
  - 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
status: public
title: Stability vs.~instability of singular steady states in the parabolic-elliptic
  Keller-Segel system on $\R^n$
type: journal_article
user_id: '31496'
year: '2023'
...
---
_id: '53333'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary
    superlinear degradation. <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>.
    Published online 2021:141-172. doi:<a href="https://doi.org/10.2422/2036-2145.202005_016">10.2422/2036-2145.202005_016</a>
  apa: Winkler, M. (2021). $L^1$ solutions to parabolic Keller-Segel systems involving
    arbitrary superlinear degradation. <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
    DI SCIENZE</i>, 141–172. <a href="https://doi.org/10.2422/2036-2145.202005_016">https://doi.org/10.2422/2036-2145.202005_016</a>
  bibtex: '@article{Winkler_2021, title={$L^1$ solutions to parabolic Keller-Segel
    systems involving arbitrary superlinear degradation}, DOI={<a href="https://doi.org/10.2422/2036-2145.202005_016">10.2422/2036-2145.202005_016</a>},
    journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola
    Normale Superiore - Edizioni della Normale}, author={Winkler, Michael}, year={2021},
    pages={141–172} }'
  chicago: Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving
    Arbitrary Superlinear Degradation.” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
    DI SCIENZE</i>, 2021, 141–72. <a href="https://doi.org/10.2422/2036-2145.202005_016">https://doi.org/10.2422/2036-2145.202005_016</a>.
  ieee: 'M. Winkler, “$L^1$ solutions to parabolic Keller-Segel systems involving
    arbitrary superlinear degradation,” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
    DI SCIENZE</i>, pp. 141–172, 2021, doi: <a href="https://doi.org/10.2422/2036-2145.202005_016">10.2422/2036-2145.202005_016</a>.'
  mla: Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving
    Arbitrary Superlinear Degradation.” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
    DI SCIENZE</i>, Scuola Normale Superiore - Edizioni della Normale, 2021, pp. 141–72,
    doi:<a href="https://doi.org/10.2422/2036-2145.202005_016">10.2422/2036-2145.202005_016</a>.
  short: M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (2021) 141–172.
date_created: 2024-04-07T12:45:49Z
date_updated: 2025-12-18T20:15:27Z
doi: 10.2422/2036-2145.202005_016
keyword:
- Mathematics (miscellaneous)
- Theoretical Computer Science
language:
- iso: eng
page: 141-172
publication: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
publication_identifier:
  issn:
  - 2036-2145
  - 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
status: public
title: $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear
  degradation
type: journal_article
user_id: '31496'
year: '2021'
...
---
_id: '63373'
article_number: 421-466
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
- first_name: Zhaoyin
  full_name: Xiang, Zhaoyin
  last_name: Xiang
citation:
  ama: Wang Y, Winkler M, Xiang Z. Global classical solutions in a two-dimensional
    chemotaxis-Navier-Stokes system with subcritical sensitivity. <i>ANNALI SCUOLA
    NORMALE SUPERIORE - CLASSE DI SCIENZE</i>. Published online 2021. doi:<a href="https://doi.org/10.2422/2036-2145.201603_004">10.2422/2036-2145.201603_004</a>
  apa: Wang, Y., Winkler, M., &#38; Xiang, Z. (2021). Global classical solutions in
    a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity.
    <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Article 421–466. <a
    href="https://doi.org/10.2422/2036-2145.201603_004">https://doi.org/10.2422/2036-2145.201603_004</a>
  bibtex: '@article{Wang_Winkler_Xiang_2021, title={Global classical solutions in
    a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity},
    DOI={<a href="https://doi.org/10.2422/2036-2145.201603_004">10.2422/2036-2145.201603_004</a>},
    number={421–466}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE},
    publisher={Scuola Normale Superiore - Edizioni della Normale}, author={Wang, Yulan
    and Winkler, Michael and Xiang, Zhaoyin}, year={2021} }'
  chicago: Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Global Classical Solutions
    in a Two-Dimensional Chemotaxis-Navier-Stokes System with Subcritical Sensitivity.”
    <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, 2021. <a href="https://doi.org/10.2422/2036-2145.201603_004">https://doi.org/10.2422/2036-2145.201603_004</a>.
  ieee: 'Y. Wang, M. Winkler, and Z. Xiang, “Global classical solutions in a two-dimensional
    chemotaxis-Navier-Stokes system with subcritical sensitivity,” <i>ANNALI SCUOLA
    NORMALE SUPERIORE - CLASSE DI SCIENZE</i>, Art. no. 421–466, 2021, doi: <a href="https://doi.org/10.2422/2036-2145.201603_004">10.2422/2036-2145.201603_004</a>.'
  mla: Wang, Yulan, et al. “Global Classical Solutions in a Two-Dimensional Chemotaxis-Navier-Stokes
    System with Subcritical Sensitivity.” <i>ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
    DI SCIENZE</i>, 421–466, Scuola Normale Superiore - Edizioni della Normale, 2021,
    doi:<a href="https://doi.org/10.2422/2036-2145.201603_004">10.2422/2036-2145.201603_004</a>.
  short: Y. Wang, M. Winkler, Z. Xiang, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI
    SCIENZE (2021).
date_created: 2025-12-19T11:05:07Z
date_updated: 2025-12-19T11:05:13Z
doi: 10.2422/2036-2145.201603_004
language:
- iso: eng
publication: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
publication_identifier:
  issn:
  - 2036-2145
  - 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
status: public
title: Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system
  with subcritical sensitivity
type: journal_article
user_id: '31496'
year: '2021'
...