Nonlinear Stability and Optimal Decay Rate for a Multidimensional Generalized Kuramoto]Sivashinsky System

We study the Cauchy problem for a generalized Kuramoto]Sivashinsky system in multidimension. The zero equilibrium is linearly stable for coefficients within a certain range. We further establish the global existence, nonlinear stability, and optimal decay rate of the solution for coefficients within the same range, though with suitable restriction to the initial data