Global existence results for the 2D Kuramoto-Sivashinsky equation

Abstract: The Kuramoto-Sivashinsky equation is a model for the motion of flame fronts. In one spatial dimension much is understood, including that solutions exist for all time. Analagous results in two dimensions are much more limited; most results in 2D assume that the domain is "thin," or approximately one-dimensional. We will give an overview of the results in one dimension and of anisotropic results in two dimensions. We will then show some global existence theorems for small data in two dimensions without making use of any anisotropy. This includes joint work with Anna Mazzucato.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom