Low regularity Sobolev well-posedness for Vlasov–Poisson
Abstract
We consider the Vlasov–Poisson equation on $ \mathbb{R}^n \times \mathbb{R}^n $ with $ n \ge 3 $. We prove local well-posedness in $ H^{s}(\mathbb{R}^n \times \mathbb{R}^n) $ with $ s> n/2-1/4 $, for initial distribution $ f_{0} \in H^{s}(\mathbb{R}^n \times \mathbb{R}^n) $ having compact support in $ v $. In particular, data not belonging to $ L^p(\mathbb{R}^n \times \mathbb{R}^n) $ for large $ p $ are allowed.
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Computational Fluid Dynamics and Aerodynamics
Publication details
- Journal / source
- Communications on Pure & Applied Analysis
- Volume
- 37
- Issue
- 0
- Pages
- 172–189
- Publication date
- 7 July 2026
- Language
- EN