98-572 Komech A., Spohn H.

Long-time asymptotics for the coupled Maxwell-Lorentz equations. (64K, LaTeX 2e) Aug 24, 98

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Abstract. We determine the long time behavior of solutions to the Maxwell-Lorentz equations, which describe a charge coupled to the electromagnetic field and subject to external time-independent potentials. The stationary solutions have vanishing magnetic field and a Coulomb type electrostatic field centered at the points of the set $Z$ at which the external force vanishes. We prove that solutions of finite energy with bounded particle trajectory converge, in suitable local energy seminorms, to the set of stationary states in the long time limit. If the set $Z$ is discrete, this implies the convergence to a definite stationary state. For an unbounded particle trajectory, at least, the acceleration vanishes for long times and the Maxwell field as seen from the particle converges to the stationary Coulomb field.

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