Handle URI:
http://hdl.handle.net/10754/598415
Title:
Global Solutions to the Coupled Chemotaxis-Fluid Equations
Authors:
Duan, Renjun; Lorz, Alexander; Markowich, Peter
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.
Citation:
Duan R, Lorz A, Markowich P (2010) Global Solutions to the Coupled Chemotaxis-Fluid Equations. Communications in Partial Differential Equations 35: 1635–1673. Available: http://dx.doi.org/10.1080/03605302.2010.497199.
Publisher:
Informa UK Limited
Journal:
Communications in Partial Differential Equations
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
10-Aug-2010
DOI:
10.1080/03605302.2010.497199
Type:
Article
ISSN:
0360-5302; 1532-4133
Sponsors:
This research is supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). R.-J. Duan would like to thank RICAM for its support during the postdoctoral studies of the year 2008-09. A. Lorz would like to acknowledge support by KAUST. P. Markowich acknowledges support from his Royal Society Wolfson Research Merit Award. The authors would like to thank the anonymous referees for their valuable comments which improved the current results so much.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDuan, Renjunen
dc.contributor.authorLorz, Alexanderen
dc.contributor.authorMarkowich, Peteren
dc.date.accessioned2016-02-25T13:20:19Zen
dc.date.available2016-02-25T13:20:19Zen
dc.date.issued2010-08-10en
dc.identifier.citationDuan R, Lorz A, Markowich P (2010) Global Solutions to the Coupled Chemotaxis-Fluid Equations. Communications in Partial Differential Equations 35: 1635–1673. Available: http://dx.doi.org/10.1080/03605302.2010.497199.en
dc.identifier.issn0360-5302en
dc.identifier.issn1532-4133en
dc.identifier.doi10.1080/03605302.2010.497199en
dc.identifier.urihttp://hdl.handle.net/10754/598415en
dc.description.abstractIn 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.en
dc.description.sponsorshipThis research is supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). R.-J. Duan would like to thank RICAM for its support during the postdoctoral studies of the year 2008-09. A. Lorz would like to acknowledge support by KAUST. P. Markowich acknowledges support from his Royal Society Wolfson Research Merit Award. The authors would like to thank the anonymous referees for their valuable comments which improved the current results so much.en
dc.publisherInforma UK Limiteden
dc.subjectA priori estimatesen
dc.subjectChemotaxisen
dc.subjectChemotaxis-fluid interactionen
dc.subjectEnergy methoden
dc.subjectGlobal solutionen
dc.subjectStokes equationsen
dc.titleGlobal Solutions to the Coupled Chemotaxis-Fluid Equationsen
dc.typeArticleen
dc.identifier.journalCommunications in Partial Differential Equationsen
dc.contributor.institutionJohann Radon Institute for Computational and Applied Mathematics, Linz, Austriaen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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