---
_id: '53315'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional
    domain  and for a given nondecreasing positive unbounded , for each  and  the
    inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula
    />This is thereafter applied to nonglobal solutions of the Keller–Segel system
    coupled to the incompressible Navier–Stokes equations through transport and buoyancy,
    and it is seen that in any such blow‐up event the corresponding population density
    cannot remain uniformly integrable over  near its explosion time.</jats:p>"
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Wang Y, Winkler M. An interpolation inequality involving $L\log L$ spaces and
    application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes
    system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a
    href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>
  apa: Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving $L\log
    L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>,
    <i>109</i>(3). <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>
  bibtex: '@article{Wang_Winkler_2024, title={An interpolation inequality involving
    $L\log L$ spaces and application to the characterization of blow‐up behavior in
    a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>},
    number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley},
    author={Wang, Yulan and Winkler, Michael}, year={2024} }'
  chicago: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving
    $L\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in
    a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London
    Mathematical Society</i> 109, no. 3 (2024). <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>.
  ieee: 'Y. Wang and M. Winkler, “An interpolation inequality involving $L\log L$
    spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, 2024, doi: <a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.'
  mla: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\log
    L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional
    Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, Wiley, 2024, doi:<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.
  short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).
date_created: 2024-04-07T12:27:28Z
date_updated: 2024-04-07T12:36:25Z
doi: 10.1112/jlms.12885
intvolume: '       109'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
publication: Journal of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6107
  - 1469-7750
publication_status: published
publisher: Wiley
status: public
title: An interpolation inequality involving $L\log L$ spaces and application to the
  characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes
  system
type: journal_article
user_id: '31496'
volume: 109
year: '2024'
...
---
_id: '63259'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional
    domain  and for a given nondecreasing positive unbounded , for each  and  the
    inequality\r\n<jats:disp-formula/>is shown to hold for any positive  fulfilling\r\n<jats:disp-formula/>This
    is thereafter applied to nonglobal solutions of the Keller–Segel system coupled
    to the incompressible Navier–Stokes equations through transport and buoyancy,
    and it is seen that in any such blow‐up event the corresponding population density
    cannot remain uniformly integrable over  near its explosion time.</jats:p>"
article_number: e12885
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Wang Y, Winkler M. An interpolation inequality involving LlogL$L\log L$ spaces
    and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>.
    2024;109(3). doi:<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>
  apa: Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving LlogL$L\log
    L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>,
    <i>109</i>(3), Article e12885. <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>
  bibtex: '@article{Wang_Winkler_2024, title={An interpolation inequality involving
    LlogL$L\log L$ spaces and application to the characterization of blow‐up behavior
    in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a
    href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>}, number={3e12885},
    journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang,
    Yulan and Winkler, Michael}, year={2024} }'
  chicago: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving
    LlogL$L\log L$ Spaces and Application to the Characterization of Blow‐up Behavior
    in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London
    Mathematical Society</i> 109, no. 3 (2024). <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>.
  ieee: 'Y. Wang and M. Winkler, “An interpolation inequality involving LlogL$L\log
    L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, Art. no. e12885, 2024, doi: <a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.'
  mla: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\log
    L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional
    Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, e12885, Wiley, 2024, doi:<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.
  short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).
date_created: 2025-12-18T19:07:25Z
date_updated: 2025-12-18T20:14:39Z
doi: 10.1112/jlms.12885
intvolume: '       109'
issue: '3'
language:
- iso: eng
publication: Journal of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6107
  - 1469-7750
publication_status: published
publisher: Wiley
status: public
title: An interpolation inequality involving LlogL$L\log L$ spaces and application
  to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes
  system
type: journal_article
user_id: '31496'
volume: 109
year: '2024'
...
---
_id: '40066'
author:
- first_name: Rodrigo
  full_name: Bañuelos, Rodrigo
  last_name: Bañuelos
- first_name: Krzysztof
  full_name: Bogdan, Krzysztof
  last_name: Bogdan
- first_name: Tomasz
  full_name: Luks, Tomasz
  id: '58312'
  last_name: Luks
citation:
  ama: Bañuelos R, Bogdan K, Luks T. Hardy–Stein identities and square functions for
    semigroups. <i>Journal of the London Mathematical Society</i>. 2016;94(2):462-478.
    doi:<a href="https://doi.org/10.1112/jlms/jdw042">10.1112/jlms/jdw042</a>
  apa: Bañuelos, R., Bogdan, K., &#38; Luks, T. (2016). Hardy–Stein identities and
    square functions for semigroups. <i>Journal of the London Mathematical Society</i>,
    <i>94</i>(2), 462–478. <a href="https://doi.org/10.1112/jlms/jdw042">https://doi.org/10.1112/jlms/jdw042</a>
  bibtex: '@article{Bañuelos_Bogdan_Luks_2016, title={Hardy–Stein identities and square
    functions for semigroups}, volume={94}, DOI={<a href="https://doi.org/10.1112/jlms/jdw042">10.1112/jlms/jdw042</a>},
    number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley},
    author={Bañuelos, Rodrigo and Bogdan, Krzysztof and Luks, Tomasz}, year={2016},
    pages={462–478} }'
  chicago: 'Bañuelos, Rodrigo, Krzysztof Bogdan, and Tomasz Luks. “Hardy–Stein Identities
    and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i>
    94, no. 2 (2016): 462–78. <a href="https://doi.org/10.1112/jlms/jdw042">https://doi.org/10.1112/jlms/jdw042</a>.'
  ieee: 'R. Bañuelos, K. Bogdan, and T. Luks, “Hardy–Stein identities and square functions
    for semigroups,” <i>Journal of the London Mathematical Society</i>, vol. 94, no.
    2, pp. 462–478, 2016, doi: <a href="https://doi.org/10.1112/jlms/jdw042">10.1112/jlms/jdw042</a>.'
  mla: Bañuelos, Rodrigo, et al. “Hardy–Stein Identities and Square Functions for
    Semigroups.” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2,
    Wiley, 2016, pp. 462–78, doi:<a href="https://doi.org/10.1112/jlms/jdw042">10.1112/jlms/jdw042</a>.
  short: R. Bañuelos, K. Bogdan, T. Luks, Journal of the London Mathematical Society
    94 (2016) 462–478.
date_created: 2023-01-25T15:43:14Z
date_updated: 2023-01-26T17:20:19Z
department:
- _id: '555'
doi: 10.1112/jlms/jdw042
extern: '1'
intvolume: '        94'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
page: 462-478
publication: Journal of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6107
  - 1469-7750
publication_status: published
publisher: Wiley
status: public
title: Hardy–Stein identities and square functions for semigroups
type: journal_article
user_id: '58312'
volume: 94
year: '2016'
...