Local well-posedness for a class of singular Vlasov equations

2022/02/15 by Thomas Chaub, Chaub, Thomas
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.2202.07287

arxiv created 2022/02/15 · openalex publication_date 2022/02/15 · arxiv updated 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study a singular Vlasov system on the torus where the force field has the smoothness of a (fractional) derivative D^α of the density, where α>0. We prove local well-posedness in Sobolev spaces without restriction on the data. This is in sharp contrast with the case α=0 which is ill-posed in Sobolev spaces for general data.

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