具混合边界条件的趋化-流体耦合模型解的整体存在性

Global solvability to a coupled chemotaxis-fluid model with mixed boundary conditions

本文考虑如下趋化-流体耦合模型的混合边值问题:■主要研究其在空间有界二维区域上解的整体存在性及一致有界性问题.首先,证明慢扩散情形(m>1)混合非齐次边值问题的一致有界弱解的整体存在性.其次,考虑线性扩散情形(m=1),对于混合齐次边值问题,得到经典解的整体存在性.

This paper is concerned with the following chemotaxis-fluid model■with mixed boundary value conditions.We mainly study the global existence and uniform boundedness of weak solutions in a bounded domain of R2.Firstly,we prove the global existence of uniformly bounded weak solutions for the porous medium slow diffusion model(m>1)with non-homogeneous boundary conditions.Then we also consider the linear diffusion case(m=1)with homogeneous boundary conditions,and prove the existence of global bounded classical solutions.