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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M. Chae, K. Kang, and J. Lee, Existence of smooth solutions to coupled chemotaxis-fluid equations, Discrete Contin. Dyn. Syst. 33 (2013), no. 6, 2271-2297.
A. Chertock, K. Fellner, A. Kurganov, A. Lorz, and P. A. Markowich, Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach, J. Fluid Mech. 694 (2012), 155-190.
R. Duan, A. Lorz, and P. Markowich, Global solutions to the coupled chemotaxis-fluid equations, Comm. Partial Differential Equations 35 (2010), no. 9, 1635-1673.
M. D. Francesco, A. Lorz, and P. Markowich, Chemotaxis-fluid coupled model for swim-ming bacteria with nonlinear diffusion: global existence and asymptotic behavior, Dis-crete Contin. Dyn. Syst. 28 (2010), no. 4, 1437-1453.
S. Ishida and T. Yokota, Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic type, J. Differential Equations 252 (2012), no. 2, 1421-1440.
E. F. Keller and L. A. Segel, Initiation of slide mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970), no. 3, 399-415.
E. F. Keller and L. A. Segel, Model for chemotaxis, J. Theor. Biol. 30 (1971), no. 2, 225-234.
O. A. Ladyzhenskaya, Global solvability of a boundary value problem for the Navier-Stokes equations in the case of two spatial variables, Doklady of the USSR 123 (1958), 427-429.
J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model, I. H. Poincare, Analyse Non Lineaire 28 (2011), no. 5, 643-652.