Lagrangian solutions to the Vlasov-Poisson system with L1 density

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Bohun, Anna¹  Bouchut, Francois²  Crippa, Gianluca¹ 

[1] Univ Basel, Dept Mathemat & Informat, Spiegelgasse 1, CH-4051 Basel, Switzerland

[2] Univ Paris Est, CNRS, Lab Anal & Math Appl, UPEM,UPEC,UMR 8050, F-77454 Marne La Vallee, France

关键词: Vlasov-Poisson system;    Lagrangian flows;    Non BV vector fields;    Superlevels;    Weakly convergent initial data;   

DOI  :  10.1016/j.jde.2015.10.041

来源: Elsevier

【 摘 要 】

The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. An a priori estimate on the smallness of the superlevels of the flow in three dimensions is established in order to control the characteristics. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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