# American Institute of Mathematical Sciences

December  2013, 6(4): 715-727. doi: 10.3934/krm.2013.6.715

## 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  February 2013 Revised  June 2013 Published  November 2013

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.
Citation: Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation. Kinetic & Related Models, 2013, 6 (4) : 715-727. doi: 10.3934/krm.2013.6.715
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