Gradient Growth for Vlasov-Poisson in background charge distributed by Desingularized Dirac Delta
Year: 2026
Type: preprint
Abstract: We prove the superlinear gradient growth for the one dimensional Vlasov-Poisson equation on the torus. We show them by first constructing the stationary solution which has a hyperbolic flow (locally). Then we perturb the solution and use the $L^\infty$ stability of the characteristic velocity field to show the superlinear growth. This proof was inspired by the work of Denisov.
Source: arXiv (Cornell University)
Author: Tae, Sangwook
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213345128