A Note on Global Existence for the Chemotaxis-Stokes Model with Nonlinear Diffusion

作者：Duan, Renjun; Xiang, Zhaoyin^*

来源：International Mathematics Research Notices, 2014, 2014(7): 1833-1852.

DOI：10.1093/imrn/rns270

• KELLER-SEGEL MODEL
• AGGREGATION

This note is concerned with the Cauchy problem on the 3D chemotaxis-Stokes equations with nonlinear diffusions and large initial data. We prove the global existence of weak solutions for all adiabatic exponents m is an element of [1,+infinity). In particular, the result fills up the gap between m = 1 by Winkler [24] and m is an element of (4/3, 2] by Liu and Lorz [16]. A similar result also holds for the 2D chemotaxis-Navier-Stokes equations.

• 出版日期2014
• 单位电子科技大学