### 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 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

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

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*Communications In Mathematical Physics*, vol. 363, no. 2, pp. 389-434. https://doi.org/10.1007/s00220-018-3208-7

**Long Time Estimates for the Vlasov–Maxwell System in the Non-relativistic Limit.** / Han-Kwan, Daniel; Nguyen, Toan T.; Rousset, Frédéric.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Long Time Estimates for the Vlasov–Maxwell System in the Non-relativistic Limit

AU - Han-Kwan, Daniel

AU - Nguyen, Toan T.

AU - Rousset, Frédéric

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85049976559&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049976559&partnerID=8YFLogxK

U2 - 10.1007/s00220-018-3208-7

DO - 10.1007/s00220-018-3208-7

M3 - Article

AN - SCOPUS:85049976559

VL - 363

SP - 389

EP - 434

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -