- 98-572 Komech A., Spohn H.
- Long-time asymptotics for the coupled
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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.