Calculus of Variations and Geometric Measure Theory
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A. Bohun - F. Bouchut - G. Crippa

Lagrangian solutions to the Vlasov-Poisson system with L^1 density

created by crippa on 19 Dec 2014
modified by bohun on 16 Feb 2016


Published Paper

Inserted: 19 dec 2014
Last Updated: 16 feb 2016

Journal: Journal of Differential Equations
Volume: 21
Year: 2015


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.


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