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Special macroscopic modes and hypocoercivity

  • Kleber Carrapatoso

    Institut Polytechnique de Paris, Palaiseau, France

  • Jean Dolbeault

    CNRS & Université Paris-Dauphine – PSL, Paris, France

  • Frédéric Hérau

    Université de Nantes, Nantes, France

  • Stéphane Mischler

    Université Paris-Dauphine – PSL, Paris, France

  • Clément Mouhot

    University of Cambridge, Cambridge, UK

  • Christian Schmeiser

    Universität Wien, Wien, Austria
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Abstract

We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes (stationary solutions and time-periodic solutions). We also prove the convergence of all solutions of the evolution equation to such non-trivial modes, with a quantitative exponential rate. This is the first hypocoercivity result with multiple special macroscopic modes with constructive estimates depending on the geometry of the potential.

Cite this article

Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau, Stéphane Mischler, Clément Mouhot, Christian Schmeiser, Special macroscopic modes and hypocoercivity. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1502