On asymptotic stability of solitons for 2D Maxwell–Lorentz equations

Abstract

We prove asymptotic stability of solitons for the 2D Maxwell–Lorentz equations with an extended charged particle. Soliton solutions correspond to the uniform motion of a particle. Our main result is as follows: the particle for large times moves asymptotically uniformly, and the Maxwell field asymptotically is the sum of the comoving field and the dispersive wave. The remainder converges to zero in the global energy norm.