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Special macroscopic modes and hypocoercivity

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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.
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Dates and versions

hal-03222748 , version 1 (10-05-2021)
hal-03222748 , version 2 (12-04-2022)
hal-03222748 , version 3 (23-06-2022)

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Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau, Stéphane Mischler, Clément Mouhot, et al.. Special macroscopic modes and hypocoercivity. 2022. ⟨hal-03222748v3⟩
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