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

2015/06/29 by Han-Kwan, Daniel, Nguyen, Toan T.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.08537

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 ε → 0, with ε 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 ε|. Second, we deduce the invalidity of the quasineutral limit in L² in arbitrarily short time.

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