A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation

Yoshinori Morimoto; Karel Pravda-Starov; Chao-Jiang Xu

doi:10.3934/krm.2013.6.715

Article Contents

2013, Volume 6, Issue 4: 715-727. Doi: 10.3934/krm.2013.6.715

This issue Previous Article Unstable galaxy models Next Article Global stability of stationary waves for damped wave equations

A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation

1.
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501
2.
Université de Cergy-Pontoise, CNRS UMR 8088, Mathématiques, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise
3.
Université de Rouen, UMR 6085-CNRS, Mathématiques, Avenue de l’Université, BP.12, 76801 Saint Etienne du Rouvray

Received: January 31, 2013

Revised: May 31, 2013

Published: November 2013

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Abstract

We consider the non-linear spatially homogeneous Landau equation with Maxwellian molecules in a close-to-equilibrium framework and show that the Cauchy problem for the fluctuation around the Maxwellian equilibrium distribution enjoys a Gelfand-Shilov regularizing effect in the class $S_{1/2}^{1/2}(\mathbb{R}^d)$, implying the ultra-analyticity and the production of exponential moments of the fluctuation, for any positive time.

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Mathematics Subject Classification: 35B65.

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