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

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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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Porous Medium Equation
Porous Media
Porous materials
Fluid
Stokes System
Degenerate Equations
Fluids
Continuous Solution
Existence of Weak Solutions
Degeneracy
Generalized Equation
System Modeling
Bacteria
Coupled System
Global Existence
Weak Solution
Three-dimension
Oxygen
Regularity
Motion

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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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 H{\"o}lder 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 H{\"o}lder 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 H{\"o}lder regularity, which is of independent interest.",
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Hölder continuity of Keller–Segel equations of porous medium type coupled to fluid equations. / Chung, Yun Sung; Hwang, Sukjung; Kang, Kyungkeun; Kim, Jaewoo.

In: Journal of Differential Equations, Vol. 263, No. 4, 15.08.2017, p. 2157-2212.

Research output: Contribution to journalArticle

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AB - 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.

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