The Kuramoto-Sivashinsky equation in R^1 and R^2: effective estimates of the high-frequency tails and higher Sobolev norms

Milena Stanislavova, Atanas Stefanov

We consider the Kuramoto-Sivashinsky (KS) equation in finite domains of the form $[-L,L{]}^d$. Our main result provides refined Gevrey estimates for the solutions of the one dimensio…