Hypocoercivity for linear kinetic equations conserving mass

Jean Dolbeault, Clément Mouhot, Christian Schmeiser

Research output: Contribution to journalArticlepeer-review

165 Scopus citations

Abstract

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $L_{2}$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Original languageEnglish (US)
Pages (from-to)3807-3828
Number of pages22
JournalTransactions of the American Mathematical Society
Volume367
Issue number6
DOIs
StatePublished - Feb 3 2015
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This work was partially supported by the French-Austrian Amadeus projectno. 13785UA, the ANR projects EVOL and CBDif-Fr, the Austrian Science Fund(project no. W8), and the European network DEASE. The second author thanksCambridge University for their hospitality and acknowledges support from AwardNo. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology(KAUST), as well as partial support from the ERC grant MATKIT.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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