数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1245-1254.doi: 10.1016/S0252-9602(12)60096-4

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PRECISE SMOOTHING EFFECTS OF HOMOGENEOUS LANDAU EQUATION IN SOBOLEV SPACES

Mohamed Najeme   

  1. Université|de Rouen, UMR-6085, Math´ematiques, 76801 Saint Etienne du Rouvray, France
  • 收稿日期:2011-03-26 出版日期:2012-05-20 发布日期:2012-05-20

PRECISE SMOOTHING EFFECTS OF HOMOGENEOUS LANDAU EQUATION IN SOBOLEV SPACES

Mohamed Najeme   

  1. Université|de Rouen, UMR-6085, Math´ematiques, 76801 Saint Etienne du Rouvray, France
  • Received:2011-03-26 Online:2012-05-20 Published:2012-05-20

摘要:

In this work, we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which implies the ultra-analytic effect of weak solutions.

关键词: Landau equation, smoothing effect of Cauchy problem, Sobolev spaces

Abstract:

In this work, we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which implies the ultra-analytic effect of weak solutions.

Key words: Landau equation, smoothing effect of Cauchy problem, Sobolev spaces

中图分类号: 

  • 35A05