Finite energy scattering for the Lorentz-Maxwell equation

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

10.1007/s00023-008-0378-4

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation 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.

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