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The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior

  • Kleber Carrapatoso

    Institut Polytechnique de Paris, Palaiseau, France
    ORCID

  • Stéphane Mischler

    Université Paris Dauphine-PSL, Paris, France; Institut Universitaire de France, Paris, France
    ORCID
The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior cover

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Abstract

We consider the Kinetic Fokker–Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with the constructive rate of the solution to the KFP equation towards the stationary state with the same mass as the initial datum.

Cite this article

Kleber Carrapatoso, Stéphane Mischler, The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (2025), published online first

DOI 10.4171/RLM/1055