Hölder continuity of Keller–Segel equations of porous medium type coupled to fluid equations

Yun Sung Chung, Sukjung Hwang, Kyungkeun Kang, Jaewoo Kim

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Abstract

We consider a coupled system consisting of a degenerate porous medium type of Keller–Segel system and Stokes system modeling the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global existence of weak solutions and Hölder continuous solutions in dimension three, under the assumption that the power of degeneracy is above a certain number depending on given parameter values. To show Hölder continuity of weak solutions, we consider a single degenerate porous medium equation with lower order terms, and via a unified method of proof expanded to generalized porous medium equations, we obtain Hölder regularity, which is of independent interest.

Original languageEnglish
Pages (from-to)2157-2212
Number of pages56
JournalJournal of Differential Equations
Volume263
Issue number4
DOIs
Publication statusPublished - 2017 Aug 15

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All Science Journal Classification (ASJC) codes

  • Analysis

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