Lagrangian solutions to the Vlasov-Poisson system with L¹ density

2014/12/19 by Anna Bohun, Gianluca Crippa, Bohun, Anna +4 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1412.6358

arxiv created 2014/12/19 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Finite element approximation to linear, second order, parabolic problems with L¹ data

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