For 3d Stokes Approximation Of The System

This paper studies the three-dimensional Stokes approximation equations in a bounded smooth domain. We concluded the following results:the existence, uniqueness and blow-up criterion of the local strong solutions.In the first chapter, the background of this paper is introduced as well as some important results obtained by the previous studies.In chapter two, using compact method, we prove the existence, uniqueness of the local strong solutions for three-dimensional Stokes approximation equations.In chapter three, we studies the three-dimensional Stokes approximation equations in a bounded smooth domain. Provided the initial date satisfy a nat-ural compatibility condition, we prove the local existence of the unique strong solutions.In chapter four, we establish a blow-up criterion for the local strong solutions of the Stokes approximation equations in terms of the gradient of the velocity, if the velocity satisfy certain condition, then a local strong solutions can be continued globally in time.At last, we conclude the paper and explore some open problems about the Stokes approximation equations.