Global Strong Solutions To The Incompressible MHD Equations

This paper mainly studies the global strong solutions to the 3D incompressible MHD equations.Besides,it studies global strong solutions to the 3D incompressible MHD equations with large potential force by using the piecewise-estimate ways.This paper can be divided into three parts:The first part introduces the background of the strong solution of the 3D incompressible MHD equation,the research status and the basic knowledge of some important theories and inequalities.In the second part,we study the problem of the existence of the strong solution of the 3D incompressible MHD equation.On the basis of the research results such as Kim and Craig,we can make the quality or density of the equation less appropriate or the kinematic viscosity is large enough,we get the global solution of the equation.In the third part,this paper studies the existence of the strong solution to the3 D incompressible MHD equation with external force.Based on the research results of symplectic existence of the three-dimensional incompressible MHD equation,combined with piecewise estimation method,the existence of the strong solution of the 3D incompressible MHD equation with external force is obtained.