### Abstract

In this paper, we study the Vlasov–Maxwell system in the non-relativistic limit, that is in the regime where the speed of light is a very large parameter. We consider data lying in the vicinity of homogeneous equilibria that are stable in the sense of Penrose (for the Vlasov–Poisson system), and prove Sobolev stability estimates that are valid for times which are polynomial in terms of the speed of light and of the inverse of size of initial perturbations. We build a kind of higher-order Vlasov–Darwin approximation, which allows us to reach arbitrarily large powers of the speed of light.

Original language | English (US) |
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Pages (from-to) | 389-434 |

Number of pages | 46 |

Journal | Communications In Mathematical Physics |

Volume | 363 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2018 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Han-Kwan, D., Nguyen, T. T., & Rousset, F. (2018). Long Time Estimates for the Vlasov–Maxwell System in the Non-relativistic Limit.

*Communications In Mathematical Physics*,*363*(2), 389-434. https://doi.org/10.1007/s00220-018-3208-7