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Pré-Publication, Document De Travail Année : 2005

Uniform bounds and exponential time decay results for the Vlasov-Poisson-Fokker-Planck system

Frederic Herau

Résumé

We consider the non-linear VPFP system with a coulombian repulsive interaction potential and a generic confining potential in space dimension $d \geq 3$. Using spectral and kinetic methods we prove existence and uniqueness of a mild solution in weighted spaces and for small charge we find an explicit exponential rate of convergence toward the equilibrium in terms of the Witten Laplacian associated to the linear equation.
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Dates et versions

hal-00004028 , version 1 (21-01-2005)
hal-00004028 , version 2 (08-02-2005)
hal-00004028 , version 3 (23-01-2008)

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Frederic Herau. Uniform bounds and exponential time decay results for the Vlasov-Poisson-Fokker-Planck system. 2005. ⟨hal-00004028v2⟩
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