Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations

Kyungkeun Kang, Hwa Kil Kim

Research output: Contribution to journalArticle

Abstract

We consider a coupled system of Keller-Segel-type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space under the assumption that initial mass is integrable and has finite entropy. As a result, we construct solutions of Keller-Segel-Navier-Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space, in the case that its initial mass is assumed to be bounded and integrable.

Original languageEnglish
Pages (from-to)2965-3004
Number of pages40
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number4
DOIs
Publication statusPublished - 2017 Jan 1

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Existence of Weak Solutions
Chemotaxis
Coupled Model
Navier Stokes equations
Fluid
Fluids
Incompressible Navier-Stokes Equations
Absolutely Continuous
Coupled System
Weak Solution
Three-dimension
Two Dimensions
Navier-Stokes Equations
Entropy
Curve

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations. / Kang, Kyungkeun; Kim, Hwa Kil.

In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 4, 01.01.2017, p. 2965-3004.

Research output: Contribution to journalArticle

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