Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

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Abstract

We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

Original languageEnglish
Pages (from-to)5360-5387
Number of pages28
JournalJournal of Differential Equations
Volume264
Issue number8
DOIs
Publication statusPublished - 2018 Apr 15

Bibliographical note

Funding Information:
H. Bae was supported by NRF-2015R1D1A1A01058892.

Funding Information:
K. Kang was supported by NRF-2017R1A2B4006484 and NRF-20151009350.

Funding Information:
S. Kim was supported by NRF-20151009350.

Publisher Copyright:
© 2018 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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