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Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system. (English) Zbl 1129.35023
Authors’ abstract: The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov-Poisson-Boltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible Navier-Stokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian.
MSC:
35F20General theory of first order nonlinear PDE
35Q35PDEs in connection with fluid mechanics
35Q60PDEs in connection with optics and electromagnetic theory
76N10Compressible fluids, general
82D10Plasmas (statistical mechanics)
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