Strong Solutions To The Fluid-particle System:Global Existence Near The Equilibrium

This paper mainly studies the motion of particles dispersed in fluid.The system is intended to describe the interactions of particles-droplets or bubbles-with a viscous and incompressible fluid.The application of this system is very extensive.Fluid-particle interaction is of primarily importance in sedimentation analysis of disperse suspensions of particles in fluids,for example the issues being the separation of the solid grains from the fluid by external forces.On the other hand,aerosols and sprays can be also modelled by fluid-particle type interactions in which bubbles of suspended substances are seen as solid particles.Eventually,such problems also arises in combustion theory,when modelling Diesel engines or rocket propulsor.We consider a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation under external forces.The coupling arises from a drag force exerted by each other.The full text is divided into three chapters.The first chapter is the introduction,expounding the research background and the main conclusions of this paper.The second chapter is mainly the preliminary preparation work,in order to demonstrate the existence of the overall solution near the equilibrium solution.The third chapter is the proof of the main conclusions of this paper.The first section gives the proof of the existence of the global solution,the second section gives the proof of regularity,and the third section is the perfection of the proof of the theorem.