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arXiv · 1504.02274

Existence of global solutions for a Keller-Segel-fluid equations with nonlinear diffusion

Yun-Sung Chung·Kyungkeun Kang
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Abstract

We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.

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Yun-Sung Chung, Kyungkeun Kang. 2015-04-09. Existence of global solutions for a Keller-Segel-fluid equations with nonlinear diffusion. https://doi.org/10.1063/1.4947107

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