Time Analyticity And Well-posedness Of Magnetohydrodynamic Equations

In this paper,the local solution of 3D magnetohydrodynamic equations on R~3×[0,1]is studied,and a new Stokes-Ossen kernel algebraic method is used to prove the time analyticity of bounded mild solutions,and we study the well-posedness for the system of magnetohydrodynamic equations in 3-dimensional mixed-norm Lebesgue spaces.That is,using some fundamental analysis theories in mixed-norm Lebesgue space such as Young’s inequality,time decaying of solutions for heat equations and the boundedness of the Helmholtz-Leray projection,we prove local well-posedness and global well-posedness of the solutions.The full text is divided into the following three chapters:In chapter 1,we mainly introduce the relevant research background of the magnetohydrodynamic equation and the background of the topic selection of this paper,and then introduce the main research content and results of this paper.In chapter 2,we obtain the analytical property of bounded mild solution on R~3×[0,1]with respect to time by means of a new Stokes-Ossen kernel algebraic method.In chapter 3,we introduced a new metric space,namely mixed norm Lebesgue space,whose norm decays to 0 at different rates in different spatial directions at infinity.We study the well-posedness for the system of magnetohydrodynamic e-quations in 3-dimensional mixed-norm Lebesgue spaces.Using some fundamental analysis theories in mixed-norm Lebesgue space such as Young’s inequality,time de-caying of solutions for heat equations and the boundedness of the Helmholtz-Leray projection,we prove local well-posedness and global well-posedness of the solutions.