Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits

Abstract

We study the instability of solutions to the relativistic Vlasov-Maxwell systems in two limiting regimes: the classical limit when the speed of light tends to infinity and the quasineutral limit when the Debye length tends to zero. First, in the classical limit $\epsilon \to 0$, with $\epsilon$ being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution $\mu$ of Vlasov-Poisson in arbitrarily high Sobolev norms, but become of order one away from $\mu$ in arbitrary negative Sobolev norms within time of order $|\log \epsilon |$. Second, we deduce the invalidity of the quasineutral limit in $L^2$ in arbitrarily short time.

References in corpus (1)

• Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension

Cited by in corpus (1)

• Ill-posedness of the hydrostatic Euler and singular Vlasov equations