@article{53315,
  abstract     = {{<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
<jats:disp-formula />is shown to hold for any positive  fulfilling
<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       = {{Wang, Yulan and Winkler, Michael}},
  issn         = {{0024-6107}},
  journal      = {{Journal of the London Mathematical Society}},
  keywords     = {{General Mathematics}},
  number       = {{3}},
  publisher    = {{Wiley}},
  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}}},
  doi          = {{10.1112/jlms.12885}},
  volume       = {{109}},
  year         = {{2024}},
}

@article{63259,
  abstract     = {{<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
<jats:disp-formula/>is shown to hold for any positive  fulfilling
<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       = {{Wang, Yulan and Winkler, Michael}},
  issn         = {{0024-6107}},
  journal      = {{Journal of the London Mathematical Society}},
  number       = {{3}},
  publisher    = {{Wiley}},
  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}}},
  doi          = {{10.1112/jlms.12885}},
  volume       = {{109}},
  year         = {{2024}},
}

@article{40066,
  author       = {{Bañuelos, Rodrigo and Bogdan, Krzysztof and Luks, Tomasz}},
  issn         = {{0024-6107}},
  journal      = {{Journal of the London Mathematical Society}},
  keywords     = {{General Mathematics}},
  number       = {{2}},
  pages        = {{462--478}},
  publisher    = {{Wiley}},
  title        = {{{Hardy–Stein identities and square functions for semigroups}}},
  doi          = {{10.1112/jlms/jdw042}},
  volume       = {{94}},
  year         = {{2016}},
}