On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics

The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)^-3/4 in L²(R³) holds for solutions of the above equations, provided that the initial data are in L²(R³)∩L¹(R³). Since the systems of equations are not rotationally invariant, the perturbation theory for one parameter family of matrices is not useful enough to derive the above result. Therefore, by exploiting an energy method, we show that the decay estimate holds for the solutions of a general class of equations of symmetric hyperbolic-parabolic type, which contains the linearized equations in both electro-magneto-fluid dynamics and magnetohydrodynamics.