Existence and regularity of a weak solution to Maxwells equations with a thermal effect

This paper deals with Maxwellʹs equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Holder continuous if the conductivity decays suitably as temperature increases. Moreover, uniqueness of the solution is proved, which gives a positive answer for a open question from the previous research. The main idea for the global existence is based on deriving various energy estimates for the solution of the coupled system.