Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

被引：0
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作者：
Xiao-jing Cai
Quan-sen Jiu*
Chun-yan Xue
机构：
[1] Capital Normal University,School of Mathematical Sciences
[2] Beijing Information Science and Technology University,Department of Mathematics
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2007年 / 23卷
关键词：
Non-homogeneous Navier-Stokes equations; Stokes approximate; weak solutions; strong solution; 35Q30; 35Q35; 76D03;
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摘要：
In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density ρ0(x) is bounded away from 0 and other appropriate assumptions (see Theorem 1 and Theorem 2). The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
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