Global Classical Solutions for the “one and One-half” Dimensional Relativistic Vlasov-maxwell-fokker-planck System
نویسندگان
چکیده
In a recent paper Calogero and Alcántara [Kinet. Relat. Models, 4 (2011), pp. 401-426] derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the “one and one-half” dimensional version of this problem with nonlinear electromagnetic interactions the relativistic Vlasov-Maxwell-Fokker-Planck system and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.
منابع مشابه
Global Classical Solutions of the “one and One-half” Dimensional
We study the “one and one-half” dimensional Vlasov–Maxwell–Fokker–Planck system and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-intime existence and uniqueness in the large of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.
متن کاملLow Field Regime for the Relativistic Vlasov-Maxwell-Fokker-Planck System; the One and One Half Dimensional Case
We study the asymptotic regime for the relativistic Vlasov-Maxwell-FokkerPlanck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in...
متن کاملKinetic Equations with Maxwell Boundary Condition
We prove global stability results of DiPerna-Lions renormalized solutions to the initial boundary value problem for kinetic equations. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which include the so-called Maxwell boundary condition, and we prove that it is realized (it is not relaxed!). The techniques are illustrated with the Fokker-Planck-Boltzmann equat...
متن کاملGlobal existence of weak and classical solutions for the Navier–Stokes–Vlasov–Fokker–Planck equations
a r t i c l e i n f o a b s t r a c t We consider a system coupling the incompressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation. The coupling arises from a drag force exerted by each other. We establish existence of global weak solutions for the system in two and three dimensions. Furthermore, we obtain the existence and uniqueness result of global smooth solutions for dimen...
متن کاملOn Classical Solutions of the Relativistic Vlasov-klein-gordon System
We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that class...
متن کامل