STABILITY OF SOLUTIONS OF THE MAGNETOHYDRODYNAMIC EQUATIONS AND CONVERGENCE TO STEADY STATE

Based on previous work of many researchers about the stability of solutions of incompressible Navier-Stokes equations as well as magnetohydrodynamic equations, we prove that the solutions of three dimensional incompressible non-stationary MHD equations are stable with respect to initial conditions. We adopt a different approach in proving this result as compared to the approach used by other researchers.

We further prove that norm of the solution of linearized MHD equations in appropriate function space approaches to zero. This result is stronger than stability result. Furthermore we also prove that the solution of non-stationary MHD equations converges to that of stationary MHD equations as t → ∞, convergence being in an appropriate function space.