Local and global existence of a nonlocal equation with a singular integral drift term

Abstract

We study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the drift term is a generalization of existing results. Making use of some important boundedness properties of Calder\'on-Zygmund operator in \(L_p\) and Lipschitz spaces, we obtain local and global existence theorems.