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

Research output: Contribution to journalArticle

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

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Viscosity Method
Stokes System
Vanishing Viscosity
Uniqueness of Solutions
Variable Coefficients
Green's function
Parabolic Equation
Porous Media
Weak Solution
Porous materials
Three-dimension
Duality
Uniqueness
Viscosity
Fluid
Fluids
Term
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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title = "Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations",
abstract = "We prove the uniqueness of H{\"o}lder 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.",
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Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations. / Bae, Hantaek; Kang, Kyungkeun; Kim, Seick.

In: Journal of Differential Equations, Vol. 264, No. 8, 15.04.2018, p. 5360-5387.

Research output: Contribution to journalArticle

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