Solution of axisymmetric Maxwell equations

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 H¹ 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).