The Inviscid Limit Of The 3D Homogeneous Incompressible Boussinesq Equations

We consider the inviscous limits for the three-dimensional nonhomogeneous incompressible Boussinesq equation in the flat region.The three-dimensional nonhomogeneous incompressible Boussinesq equation can describe the law of fluid motion.The problem of viscosity vanishing limit has a strong physical background,it is one of the important mathematical problems in the field of hydrodynamics.When considering the relevant boundary conditions,the mathematical research is challenging.In this paper,we generalize the theory of inviscid limit problem for incompressible Navier Stokes equation.This paper is mainly divided into five parts to expand some basic properties and bases of three-dimensional nonhomogeneous incompressible Boussinesq equation.The basic theoretical research is mainly embodied in the establishment of uniform estimation theory and the proof of convergence estimation.The details are as follows:In the first chapter,we introduce the problems to be studied,the research progress and the research status.The results of the study and the arrangement of the main contents are introduced.In the second chapter,we introduce some basic symbols,Stokes operators and related inequalities.Stokes operator theory lays the foundation for the well posedness of the solution,so we only give a priori estimate for the solution.In the third chapter,we introduce the case of flat region,generalize the boundary conditions to the case of higher dimension,and provide the basis for the establishment of higher-order theory.In Chapter 4,we prove the a prior estimation and get the uniformly estimation result.In Chapter 5,we discuss the solution of the three-dimensional nonhomogeneous incompressible Boussinesq equation converge to that of the three-dimensional nonhomogeneous incompressible Boussinesq Euler equation,and establish the estimation of the convergence rate.