Global well-posedness for the four-dimensional repulsive Vlasov--Poisson system and for Vlasov--Riesz equations
Year: 2026
Type: preprint
Abstract: We establish global classical well-posedness for the four-dimensional repulsive Vlasov--Poisson system, for every nonnegative \(f_0\in C_c^1(\mathbb{R}^8)\). We also prove global well-posedness for Vlasov equations with power-law interactions for \(d\ge4\). For every \(0<α<3\), we treat both attractive and repulsive interactions with arbitrary nonnegative, compactly supported bounded initial data. Neither result requires a smallness assumption on the initial data. For attractive interactions, a virial argument yields finite-time breakdown for negative-energy solutions when \(3\leα
Source: arXiv (Cornell University)
Author: Katriadakis, Emmanouil
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212116225