非弹性的带外场Boltzmann方程和VPB方程的Cauchy问题.pdfVIP

Abstract Boltzmann build Boltzmann equation which based on Maxwell [1,2] and other work in 1872 [3] . Boltzmann equation can be used to describe the evolution of rarefied gas.The external force or in the self-consistent gravitational repulsion effect can be described by Boltzmann equation with external force and Vlasov-Poisson-Boltzmann( VPB for short). According to whether the energy loss in the collision process can be divided into two cases of elastic and inelastic. There are a large number of charged particles in the universe, Charged particles exist not only between the short-range force (collision) the existence of Coulomb static electricity and gravitation. Coulomb electrostatic is greater than the gravitational force and thus the role of gravity can be ignored, and the Coulomb electrostatic interactions and collisions decided State of the charged particles and particle interactions in the induced electric field by the collision and the Boltzmann equation can only be simulated touch Hit role for the role of the Coulomb electrostatic force will fail. VPB equation can describe the Coulomb electrostatic force and the collision of these two kind of force, which is used to simulate the thin charged particle state. We consider the existence and stability under soft potential of inelastic Boltzmann equation with external force and the VPB equation.Elasticity coefficient is constant and its range is constants. First of all, We obtain the estimate of the collision operator of external Boltzmann equation. Second, we construct a mapping of the Banach space and prove its compression.Boltzmann equation with external force has classic solution could be proved by Banach fixed point theorem.The uniform stability of Boltzmann equation with external force can be obtained by mild form of it and collision operator estimate. We obta