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Archive for the ‘Plasma Physics’ Category

(this post was also posted here on my new blog address:http://blog.toannguyen.org/ )

Daniel Han-Kwan and I have just submitted a paper entitled: “Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits”, which is also available on arxiv: arXiv:1506.08537. In this paper, 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 \rightarrow 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 {\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 \varepsilon|}. Second, we deduce the invalidity of the quasineutral limit in {L^2} in arbitrarily short time.

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