Research On Some Mathematical Problems Of Micropolar Fluid Model

In this article,we study two mathematical problems of one-dimensional compressible micropolar fluid model.This article is mainly composed by three parts:In the first chapter,we make a brief introduction of application background and significance of theoretical research?to the micropolar fluid model.First of all,we propose the problems to be studied and list the ways to overcome them;secondly,we give some basic definitions and inequalities that will be used in this article.In the second chapter,we introduce the existing results related to the micropolar fluid model and bring out the first question : the large-time behavior of solutions to the inflow problem for the one-dimensional compressible micropolar fluid model in a half line.By carefully observing the relationship between the micropolar fluid model and the Navier-Stokes equation,we construct a composite wave which satisfy compatibility conditions,then let the solutions of the model and the composite wave to construct the disturbance equation and then reconstruct the inflow problem.The main conclusion is: we obtain the global existence of solutions on the basic energy method.By using a priori estimates,we prove that the composite wave consisting of the transonic boundary layer solution,the 1-rarefaction wave,the viscous contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotically stable under some smallness conditions.In the third chapter,we study the large-time behavior of the solutions to the initial boundary value problem of the one-dimensional compressible micropolar fluid model in the whole space under large initial data.The main conclusion is: the global solutions is asymptotically stable as time tends to infinity by using elementary energy methods,the uniform positive lower and upper bounds of density and temperature.