The Global Existence Of Weak Solutions Of The Two-dimensional Stokes Approximation System

In this paper, we consider the existence of global weak solutions to the Two-dimensional Stokes approximation system. The Stokes approximation system is one of the best-known simplifications of the Navier-Stokes equations. It is a good approximation for strongly viscous fluids.This paper is organized as follow:In chapter one, the background of this paper and basic knowledge are in-troduced as well as the main conclusion in this paper.In chapter two, whenγ=1, we prove the existence of global weak solutions to the Stokes approximation system. First, we add the artificial viscosity term on the momentum equation of Stokes approximation system, and construct the approximation problem; then we derive some priori estimates, and use them to take limit for the artificial viscosity term; at last, we prove weak limit namely for the global weak solutions of the Stokes approximation system.In chapter three, whenγ>1, we prove the existence of global weak solutions to the Stokes approximation system. Our method is the same as E.Feireisl, A.Novotny and H. Petzeltovd's paper. But the difference lies in the order of passing to limit. E.Feireisl passed to the limit for nâ†'∞, before he passed to limit for eâ†'0. But in this paper, we first fix n and pass to the limit for eâ†'0, then we let nâ†'∞. Our method overcomes some of the difficulties E.Feireisl encountered. We simplify the process of passing to the limit.