Phase space of a model of magnetohydrodynamics of nonzero order

Abstract

We describe the phase space of the first initial–boundary value problem for a system of partial differential equations modeling the motion of an incompressible viscoelastic Kelvin–Voigt fluid of nonzero order in the Earth magnetic field. In the framework of the theory of semilinear equations of Sobolev type, we prove the existence and uniqueness of a solution that is a quasistationary semitrajectory.