Global Solutions to the Coupled Chemotaxis-Fluid Equations

Renjun Duan, Alexander Lorz, Peter A. Markowich

Research output: Contribution to journalArticlepeer-review

208 Scopus citations

Abstract

In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the Chemotaxis-Navier-Stokes system over three space dimensions, we obtain global existence and rates of convergence on classical solutions near constant states. When the fluid motion is described by the simpler Stokes equations, we prove global existence of weak solutions in two space dimensions for cell density with finite mass, first-order spatial moment and entropy provided that the external forcing is weak or the substrate concentration is small. © Taylor & Francis Group, LLC.
Original languageEnglish (US)
Pages (from-to)1635-1673
Number of pages39
JournalCommunications in Partial Differential Equations
Volume35
Issue number9
DOIs
StatePublished - Aug 10 2010
Externally publishedYes

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