Nonlinear instability in Vlasov type equations around rough velocity profiles
Analysis of PDEs
2018-11-06 v1
Abstract
In the Vlasov-Poisson equation, every configuration which is homogeneous in space provides a stationary solution. Penrose gave in 1960 a criterion for such a configuration to be linearly unstable. While this criterion makes sense in a measure-valued setting, the existing results concerning nonlinear instability always suppose some regularity with respect to the velocity variable. Here, thanks to a multiphasic reformulation of the problem, we can prove an "almost Lyapounov instability" result for the Vlasov-Poisson equation, and an ill-posedness result for the kinetic Euler equation and the Vlasov-Benney equation (two quasineutral limits of the Vlasov-Poisson equation), both around any unstable measure.
Keywords
Cite
@article{arxiv.1811.01350,
title = {Nonlinear instability in Vlasov type equations around rough velocity profiles},
author = {Aymeric Baradat},
journal= {arXiv preprint arXiv:1811.01350},
year = {2018}
}