GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION Chung, Yun-Sung; Kang, Kyungkeun; Kim, Jaewoo;
We consider the Cauchy problem for a Keller-Segel-fluid model 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.
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ASYMPTOTIC BEHAVIORS OF SOLUTIONS FOR AN AEROTAXIS MODEL COUPLED TO FLUID EQUATIONS, Journal of the Korean Mathematical Society, 2016, 53, 1, 127
Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion, Journal of Mathematical Physics, 2016, 57, 4, 041503
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