New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations
New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations
We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from a previous paper of the third author, at the same time slightly improving the result. That result relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the …