On Classical Solutions Of The Two-species Vlasov-poisson System In R~2 With Infinite Charge

Plasma is composed of a large number of charged particles not coherent system when the movement of the movement of the plasma and the electric field of tightly coupled,there is a very rich collection effect and collective sports model we can use Vlasov-Poisson equation to describe the motion of particles in this article main research: in the two-dimensional case,the two components of Vlasov-Poisson system of infinite charge problems.Firstly,we introduce the research background of the classical Vlasov-Poisson system and the research status of infinite Charge problems.Secondly,we give the core conclusions of this paper and the prior estimates that need to be used later.Assuming that the initial conditions are satisfied: the phase space density of the opposite charge decays polynomially along the velocity direction only,while the net charge density decays polynomially along the velocity and space direction.then the electrostatic field is well-posed,we can study its infinite charge problem in this paper.we study the Vlasov-Poisson system of two components with opposite charge,We use the method of compression mapping to study it.By referring to the previous methods and making proper extension,we prove the local existence and uniqueness of the classical solution of infinite charge problem in two-dimensional case and establish the continuation criterion.Finally,we summarize the paper and point out some problems that can be further studied in the future.