Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

This work establishes global regularity for the fractional heat equation in parabolic Bessel-potential and fractional Sobolev spaces. It also proves compactness of the solution operator and applies the resulting estimates to existence and regularity questions for a class of Kardar-Parisi-Zhang equations with fractional diffusion and a nonlocal gradient term.

Editorial status: Under review. A public preprint is available on arXiv.