The Investigation Of The Well-posedness Of The Solutions To Fluid Mechanicsc Quations

The basic series of equations in theoretical fluid mechanics is Navier-Stokes equations.If the magnetic field is considered,then the fluid mechanics equations is mainly characterized by the MHD equations.The study of fluid mechanics equations which are used to describe the mechanics behavior of some fluids substance,such as liquid and gas,and show the dynamic balance among all kinds of force acting on any given domian in fluid,is a hot topic in recent decades.In this paper,we study the global existence and large-time behavior of solutions to Navier-Stokes equations with temperature dependent heat conductivity,as well as global existence of the solution to MHD equations for Cauchy problem in one-dimensional space.We also study the existence of global smooth solution of three-dimensional space axially symmetric nonho-mogeneous incompressible MHD equations with density-dependent viscosity.The main result are as follows:· Global solution and large-time behavior of solution to Navier-Stokes equations with temperature dependent heat conductivity in one-dimensional space are obtained.Firstly,we prove v(x,t)and ?(x,t)are bounded from below and above,then we prove the solution is global-ly existence for Cauchy problem,as well as the large-time behavior of solution.· Global solution to MHD equations with temperature dependent heat conductivity in one-dimensional space is obtained.· The axially symmetric nonhomogeneous incompressible MHD equations with density-dependent viscosity in three-dimensional space are studied.Firstly,we propose a new one-dimensional model which approximates the incompressible MHD equations and prove the global regularity of the one-dimensional model,then global regularity of the three-dimensional MHD equations structured by the one-dimensional model is proved.