Existence Of Solutions To Initial Boundary Value Problems For Compressible Navier-Stokes-Smoluchowski Equations

Models of interaction between particles and compressible fluids in aerosol spray,wastewater recovery,mineral treatment,atmosphere Pollution,as well as diesel engines and rocket propulsion devices and many other fields have practical applications.This dissertation is studied the existence of solutions for compressible Navier-Stokes-Smoluchowski equations under the reasonable physical assumptions of initial values,physical domains and external forces.The equation studied describes the viscous compressible fluid dispersed in the process of particle evolution.Through the friction force of the interaction between the fluid and the particle,the coupling between the fluid motion equation and the particle equation is obtained.The model depends on the mass conservation equation,the equation representing the equilibrium momentum and the Smoluchowski equation for the equilibrium particle density.It is divided into three chapters.In Chapter 1,the research background and significance,research status at home and abroad,research content,research ideas and the main conclusions of this paper.are introduced.In Chapter 2,the definitions of theorems and the basic inequalities used in this paper are mainly introduce.In Chapter 3,the existence of solutionis proved.The first section gives the existence of solutions of the linear approximate equation of the original equation;the second section finds the boundary of the linear approximate equation independent of ? by using Young inequality,H¨older inequality and so on;the third section proves the existence and uniqueness of the solution of the linear vacuum equation;the fourth section obtains the existence of the solution of the nonlinear equation by using Sobolev embedding theorem and partial integral by iterative method.Concerning the existence of solutions for Navier-Stokes-Smoluchowski equations under certain conditions,many important results have been obtained.In this paper,we obtain the existence of strong solutions for unbounded regions.To some extent,the research results in the relevant literature are extended to more general cases.