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1986•Annales Scientifiques de l École Normale SupérieureOpen access

Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions

Pierre Degond

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Abstract

In this paper, we propose a deterministic proof of the existence of global in time smooth solutions for the Vlasov-Fokker-Planck equations.The method relies on direct estimates of the decay of the solution when the velocity goes to infinity.It also yields a proof of the convergence of the solutions, towards those of the Vlasov-Poisson equation, when the diffusion coefficient goes to zero.ACKNOWLEDGEMENTS.-I am very grateful to Pr. C. Bardos and F

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What this paper is about

In this paper, we propose a deterministic proof of the existence of global in time smooth solutions for the Vlasov-Fokker-Planck equations.The method relies on direct estimates of the decay of the solution when the velocity goes to infinity.It also yields a proof of the convergence of the solutions, towards those of the Vlasov-Poisson equation, when the diffusion coefficient goes to zero.ACKNOWLEDGEMENTS.-I am very grateful to Pr. C. Bardos and F

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Available abstract

In this paper, we propose a deterministic proof of the existence of global in time smooth solutions for the Vlasov-Fokker-Planck equations.The method relies on direct estimates of the decay of the solution when the velocity goes to infinity.It also yields a proof of the convergence of the solutions, towards those of the Vlasov-Poisson equation, when the diffusion coefficient goes to zero.ACKNOWLEDGEMENTS.-I am very grateful to Pr. C. Bardos and F

Key concepts: Fokker–Planck equation, Space (punctuation), Vlasov equation, Mathematics, Physics, Mathematical physics, Partial differential equation, Mathematical analysis

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