The Existence And Regularity Of Solutions For A Class Of Micropolar Fluid Flow Equations

This paper mainly studies two problems.Firstly,we discuss the existence of small initial solutions for two-dimensional fractional micropolar fluid flow equations.Secondly,we study the regularity of the solution of the three-dimensional micropolar fluid flow equations.The paper mainly use the spectral decomposition and Littlewood-Paley decomposition methods.In the first chapter,we introduce the research background,significance of this problem and the current research situation.We also present some conclusions of this paper and the classical inequalities.In the second chapter,we mainly study the existence of solutions for the initial value problem of incompressible two-dimensional fractional micropolar fluid flow equations We use the method of spectral decomposition to obtain the decay estimate of semigroup,and obtain the existence theorem by using fixed-point theorem.In the third chapter,we study the regularity of solutions of the three-dimensional micropolar fluid flow equations:We use the method of Littlewood-Paley decomposition to estimate the nonlinear term,and then use the iterative method to obtain the regularity of the solution of the system.Finally,we conclude the problems to be solved in the future...