Solution of axisymmetric Maxwell equations

Abstract

Abstract In this article, we study the static and time‐dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in ( Math. Meth. Appl. Sci. 2002; 25 : 49), we investigate the decoupled problems induced in a meridian half‐plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H 1 component‐wise. It is proven that the singular parts are related to singularities of Laplace‐like or wave‐like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space–time regularity results for the electromagnetic field. This paper is the continuation of ( Modél. Math. Anal. Numér . 1998; 32 : 359, Math. Meth. Appl. Sci . 2002; 25 : 49). Copyright © 2003 John Wiley & Sons, Ltd.