Low regularity Sobolev well-posedness for Vlasov--Poisson

Key Points

• Local well-posedness is achieved for the Vlasov–Poisson equation in high dimensions, enabling broader initial conditions.
• Results demonstrate well-posedness in Sobolev spaces for initial distribution with compact support in velocity, enhancing understanding of solution behavior.
• The findings imply that even data outside conventional L^p spaces can be managed within the Sobolev framework, expanding treatment possibilities.
• This study fundamentally enhances the analysis of kinetic equations by addressing low regularity scenarios, aiding future research.