Investigation of Convection Flows in an Electromagnetic Field

We investigate the solvability of an initial-boundary-value problem for a system of equations of hydrodynamics taking into account the heat transfer and displacement currents in the Maxwell equation system. Under certain conditions, we prove the global (in time) unique solvability of this problem in weighted functional spaces. Moreover, we prove that the problem can be considered as a regularly perturbed initial-boundary-value problem in which the electroconductivity of a solid medium plays the role of a small parameter.Dedicated to the Memory of Olga Aleksandrovna LADYZHENSKAYA__________Translated from Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 493–545, October–December, 2004.