A COUPLED KELLER-SEGEL-STOKES MODEL: GLOBAL EXISTENCE FOR SMALL INITIAL DATA AND BLOW-UP DELAY

Alexander Lorz

doi:10.4310/cms.2012.v10.n2.a7

A COUPLED KELLER-SEGEL-STOKES MODEL: GLOBAL EXISTENCE FOR SMALL INITIAL DATA AND BLOW-UP DELAY

Alexander Lorz

Research output: Contribution to journal › Article › peer-review

109 Scopus citations

Abstract

We study a system consisting of the elliptic-parabolic Keller-Segel equations coupled to Stokes equations by transport and gravitational forcing. We show global-in-time existence of solutions for small initial mass in 2D. In 3D we establish global existence assuming that the initial L(3/2)-norm is small. Moreover, we give numerical evidence that for this extension of the Keller-Segel system in 2D, solutions exist with mass above 8 pi, which is the critical mass for the system without fluid.

Original language	English (US)
Pages (from-to)	555-574
Number of pages	20
Journal	COMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume	10
Issue number	2
DOIs	https://doi.org/10.4310/cms.2012.v10.n2.a7
State	Published - 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-09-17
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: King Abdullah University of Science & Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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10.4310/cms.2012.v10.n2.a7

Cite this

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title = "A COUPLED KELLER-SEGEL-STOKES MODEL: GLOBAL EXISTENCE FOR SMALL INITIAL DATA AND BLOW-UP DELAY",

abstract = "We study a system consisting of the elliptic-parabolic Keller-Segel equations coupled to Stokes equations by transport and gravitational forcing. We show global-in-time existence of solutions for small initial mass in 2D. In 3D we establish global existence assuming that the initial L(3/2)-norm is small. Moreover, we give numerical evidence that for this extension of the Keller-Segel system in 2D, solutions exist with mass above 8 pi, which is the critical mass for the system without fluid.",

author = "Alexander Lorz",

note = "KAUST Repository Item: Exported on 2021-09-17 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: King Abdullah University of Science & Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AB - We study a system consisting of the elliptic-parabolic Keller-Segel equations coupled to Stokes equations by transport and gravitational forcing. We show global-in-time existence of solutions for small initial mass in 2D. In 3D we establish global existence assuming that the initial L(3/2)-norm is small. Moreover, we give numerical evidence that for this extension of the Keller-Segel system in 2D, solutions exist with mass above 8 pi, which is the critical mass for the system without fluid.

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A COUPLED KELLER-SEGEL-STOKES MODEL: GLOBAL EXISTENCE FOR SMALL INITIAL DATA AND BLOW-UP DELAY

Abstract

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ASJC Scopus subject areas

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