Abstract.
We prove global existence and uniqueness of classical solutions for the Maxwell-Lorentz system of a nonrotating rigid charge distribution, i.e.the relativistic dynamics of a nonrotating extended electron, which is subject to its own electromagnetic fields and an external potential. Local existence and uniqueness is achieved via the contraction mapping principle. Suitable a-priori-bounds yield global existence. We show that in case of a negative bare mass and an attracting external potential the stationary solution is unstable. We believe that this result clarifies the origin of the so-called "runaway"-solutions, which appear when the limit to a point charge is taken, formally described by the so called Lorentz-Dirac equation for the radiating electron.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Submitted 28/01/99, accepted 18/09/00
Rights and permissions
About this article
Cite this article
Bauer, G., Dürr, D. The Maxwell-Lorentz System of a Rigid Charge. Ann. Henri Poincaré 2, 179–196 (2001). https://doi.org/10.1007/PL00001030
Published:
Issue Date:
DOI: https://doi.org/10.1007/PL00001030