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arXiv · 1506.08537

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

Daniel Han-Kwan·Toan T. Nguyen
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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 $\varepsilon \to 0$, with $\varepsilon$ being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution $μ$ of Vlasov-Poisson in arbitrarily high Sobolev norms, but become of order one away from $μ$ in arbitrary negative Sobolev norms within time of order $|\log \varepsilon|$. Second, we deduce the invalidity of the quasineutral limit in $L^2$ in arbitrarily short time.

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Daniel Han-Kwan, Toan T. Nguyen. 2017-07-18. Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits. https://arxiv.org/abs/1506.08537

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