### Abstract

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation.

Original language | English (US) |
---|---|

Pages (from-to) | 927-943 |

Number of pages | 17 |

Journal | Annales Henri Poincare |

Volume | 9 |

Issue number | 5 |

DOIs | |

State | Published - Aug 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics

### Cite this

**Finite energy scattering for the Lorentz-Maxwell equation.** / Germain, Pierre.

Research output: Contribution to journal › Article

*Annales Henri Poincare*, vol. 9, no. 5, pp. 927-943. https://doi.org/10.1007/s00023-008-0378-4

}

TY - JOUR

T1 - Finite energy scattering for the Lorentz-Maxwell equation

AU - Germain, Pierre

PY - 2008/8

Y1 - 2008/8

N2 - In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation.

AB - In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation.

UR - http://www.scopus.com/inward/record.url?scp=50849122334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50849122334&partnerID=8YFLogxK

U2 - 10.1007/s00023-008-0378-4

DO - 10.1007/s00023-008-0378-4

M3 - Article

VL - 9

SP - 927

EP - 943

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -