Global existence of weak solutions for a Keller-Segel-fluid model with nonlinear diffusion

Yun-Sung Chung; Kyungkeun Kang; Jaewoo Kim

doi:10.4134/JKMS.2014.51.3.635

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2014; 51(3): 635-654

Printed May 1, 2014

https://doi.org/10.4134/JKMS.2014.51.3.635

Global existence of weak solutions for a Keller-Segel-fluid model with nonlinear diffusion

Yun-Sung Chung, Kyungkeun Kang, and Jaewoo Kim

Yonsei University, Yonsei University, Sungkyunkwan University

Abstract

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Abstract

We consider the Cauchy problem for a Keller-Segel-fluid mo\-del with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.\bigskip

Keywords: incompressible fluid, Keller-Segel model, nonlinear diffusion

MSC numbers: Primary 35Q30, 35Q35