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

Author： Cai Xiao-jing  

Publisher： Springer Publishing Company

ISSN： 0168-9673

Source： Acta Mathematicae Applicatae Sinica, Vol.23, Iss.4, 2007-10, pp. : 637-650

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Abstract

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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