Global Solutions Of Two Types Of Kinetic Equations With Infinite Mass

In the frame of statistical mechanics,Vlasov equation is the kinetic equation which describe the macroscopic physical properties of particle system.The model can be applied to describing the high temperature plasma.When the electrical field couples the particle system,the Vlasov-Poisson system can describe the moving process of particle.Additionally,the collisionless plasma can be described by another basic model—Vlasov-Helmholtz equation.In this paper,we mainly study the three dimensional Vlasov-Helmholtz system and Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass.In chapter one,based on the related literatures,we mainly introduce the physical background,contents,methods and progress of the research about the Vlasov-Poisson system,Vlasov-Helmholtz system and Vlasov-Poisson plasma interacting with a positive point charge.In chapter two,we are concerned with the three dimensional Vlasov-Poisson plasma interacting with a positive point charge.There are many consulted literatures for the problem of Vlasov-Poisson system with infinite mass,and the local energy as a fundamental tool is widely used to deal with the problem of infinite mass in these literatures.In this chapter,on the premise of the initial data compactly supported in velocities,we prove the global existence and uniqueness of the classical solution to the system by assuming that the initial macroscopic density slightly decays in space.Furthermore,the proof is carried out with the aid of the tool—local energy and the new introduced energy function.In the third and fourth chapter,the three dimensional Vlasov-Helmholtz system and Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass are discussed respectively on the premise of the initial data having unbounded support in the velocities.In the third chapter,it benefits the theoretic basis obtained in chapter two that we prove the global existence and uniqueness of the classical solution to the three dimensional Vlasov-Poisson plasma interacting with a positive point charge by assuming that the initial density has gaussian decay in the velocities and slightly decays in space.In the fourth chapter,we put forward some certain constraints for the local energy and assume that the initial density strongly decays in velocities,thus we establish the global existence and uniqueness of the classical solution to the Vlasov-Helmholtz system.At the end of the paper,we summarize the contents of research in this paper,meanwhile,we list some problems worth studying.