Well-posedness of fully nonlinear and nonlocal critical parabolic equations

TL;DR

This paper establishes the existence of smooth solutions for fully nonlinear, nonlocal critical parabolic equations, extending the understanding of such equations with the help of advanced a priori estimates.

Contribution

It provides a new proof of well-posedness for a class of complex nonlinear nonlocal parabolic equations using fractional diffusion estimates.

Findings

Existence of smooth solutions proven

Utilizes a priori Hölder estimates from fractional diffusion theory

Extends well-posedness results to critical nonlocal equations

Abstract

In this paper we prove the existence of smooth solutions to fully nonlinear and nonlocal parabolic equations with critical index. The proof relies on the apriori H\"older estimate for advection fractional-diffusion equation established by Silvestre \cite{Si2}.