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Article Dans Une Revue Kinetic and Related Models Année : 2018

Invariant measures for a stochastic Fokker-Planck equation

Résumé

We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when the noise intensity is sufficiently small, the system with prescribed mass admits a unique invariant measure which is exponentially mixing. The proof uses hypocoercive decay estimates and hypoelliptic gains of regularity. At last we also exhibit an explicit example showing that some restriction on the noise intensity is indeed required.
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Dates et versions

hal-01135504 , version 1 (25-03-2015)
hal-01135504 , version 2 (07-06-2019)

Identifiants

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Sylvain de Moor, Luis Miguel Miguel Rodrigues, Julien Vovelle. Invariant measures for a stochastic Fokker-Planck equation. Kinetic and Related Models , 2018, 11 (2), pp.357--395. ⟨10.3934/krm.2018017⟩. ⟨hal-01135504v1⟩
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