Research On Regularity Criterion And Well-posedness Of Fluid Model Related To MHD Equation

Hydrodynamic equations are important research areas for partial differential equations.This thesis is dedicated to the study of regularity criteria and well-posedness of fluid models related to MHD equations.The main contents are as follows:In chapter 1,it mainly introduces the research background and significance of fluid model related to MHD equation in fluid dynamics,the current status of research at home and abroad,the existing research problems and the main content of this paper.In chapter 2,the preliminary knowledge is introduced.The main contents include related basic knowledge,functional spaces,several common inequalities and the theory of Littlewood-Paley and important lemmas.In chapter 3,the regularity criterion of weak solutions of 3D MHD equations is studied.Using the method of energy estimation and several types of inequalities,a regularity criterion for the three-dimensional equations described by the horizontal velocity field and the horizontal magnetic field is obtained in the BMO space.In chapter 4,the Cauchy problem of the three-dimensional magnetic micropolar fluid equation is studied,and a new blasting criterion for improving the logarithm of the magnetic micropolar fluid equation is established in Lorentz space.In chapter 5,the whole well-posedness of the small initial value of the magnetic micropolar fluid equation in the critical Besov space is studied.Through the transformation of the equations and the Fourier localization method,the existence of a class of global solutions with a high initial value of the system is obtained.In chapter 6,the main results of the full text are summarized and the main innovations of the paper and the future research direction of the problems made in this paper are proposed.