Stability analysis of inclined plane flow and magnetohydrodynamic inclined plane flow

In this paper, we study the liquid flow down an inclined plane and prove that the the system is exponentially stable for some wave number k using the Lyapunov energy analysis approach. In addition, we introduce a new model called the magnetohydrodynamic inclined plane flow by adding the effect of a transverse magnetic field. The stability analysis of the system is achieved by the same method.