Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

Kleber Carrapatoso

doi:10.1016/j.bulsci.2014.12.002

Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

Kleber Carrapatoso

Université Paris Dauphine

Research output: Contribution to journal › Article › peer-review

Abstract

This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials. We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearised operator. This result improves the polynomial in time convergence obtained by Desvillettes and Villani [5]. Our approach is based on new decay estimates for the semigroup generated by the linearised Landau operator in weighted (polynomial or stretched exponential) L^p-spaces, using a method developed by Gualdani, Mischler and Mouhot [7].

Original language	English
Pages (from-to)	777-805
Number of pages	29
Journal	Bulletin des Sciences Mathematiques
Volume	139
Issue number	7
DOIs	https://doi.org/10.1016/j.bulsci.2014.12.002
Publication status	Published - 1 Oct 2015
Externally published	Yes

Keywords

Exponential decay
Hard potentials
Hypodissipativity
Landau equation
Spectral gap

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10.1016/j.bulsci.2014.12.002

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title = "Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials",

abstract = "This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials. We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearised operator. This result improves the polynomial in time convergence obtained by Desvillettes and Villani [5]. Our approach is based on new decay estimates for the semigroup generated by the linearised Landau operator in weighted (polynomial or stretched exponential) Lp-spaces, using a method developed by Gualdani, Mischler and Mouhot [7].",

keywords = "Exponential decay, Hard potentials, Hypodissipativity, Landau equation, Spectral gap",

author = "Kleber Carrapatoso",

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N2 - This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials. We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearised operator. This result improves the polynomial in time convergence obtained by Desvillettes and Villani [5]. Our approach is based on new decay estimates for the semigroup generated by the linearised Landau operator in weighted (polynomial or stretched exponential) Lp-spaces, using a method developed by Gualdani, Mischler and Mouhot [7].

AB - This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials. We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearised operator. This result improves the polynomial in time convergence obtained by Desvillettes and Villani [5]. Our approach is based on new decay estimates for the semigroup generated by the linearised Landau operator in weighted (polynomial or stretched exponential) Lp-spaces, using a method developed by Gualdani, Mischler and Mouhot [7].

KW - Exponential decay

KW - Hard potentials

KW - Hypodissipativity

KW - Landau equation

KW - Spectral gap

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ER -

Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

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Keywords

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