### 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 systems 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 L^{2} in arbitrarily short time.

Original language | English (US) |
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Pages (from-to) | 3444-3466 |

Number of pages | 23 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 48 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2016 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics