Uniform regularity and vanishing viscosity limit for the chemotaxis-Navier-Stokes system in a 3D bounded domain
Uniform regularity and vanishing viscosity limit for the chemotaxis-Navier-Stokes system in a 3D bounded domain
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3D 有界域中趋化-纳维-斯托克斯系统的均匀规律性和消失粘度极限
DOI：
10.1002/mma.4547
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发表时间：
2017
影响因子：
2.9
通讯作者：
Zhipeng Zhang
中科院分区：
文献类型：
--
作者：
Zhipeng Zhang
研究了三维有界域内不可压缩趋化性-Navier-Stokes系统的速度场采用Navier边界条件，细胞密度和化学浓度满足Neumann边界条件的一致正则性和零粘性极限。证明了不可压缩趋化性-Navier-Stokes系统在有限时间区间内存在唯一的与粘性系数无关的强解。此外，该解在共范Sobolev空间中一致有界，这使得我们可以取消失的粘性极限来得到不可压缩趋化-欧拉系统。
We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis‐Navier‐Stokes system with Navier boundary condition for velocity field and Neumann boundary condition for cell density and chemical concentration in a 3D bounded domain. It is shown that there exists a unique strong solution of the incompressible chemotaxis‐Navier‐Stokes system in a finite time interval, which is independent of the viscosity coefficient. Moreover, this solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible chemotaxis‐Euler system.