Global Existence and Decay of Solutions to the Fokker-Planck-Boltzmann Equation

Abstract

The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated. When the initial data is a small perturbation of an equilibrium state, global existence and optimal temporal decay estimates of classical solutions are established. Our analysis is based on the coercivity of the Fokker-Planck operator and an elementary weighted energy method.

26 pages

References in corpus (5)

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• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
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• Explicit coercivity estimates for the linearized Boltzmann and Landau operators
• Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in the Whole Space