Gradient estimates and existence of mean curvature flow with transport term

Abstract

In this paper we consider a hypersurface of the mean curvature flow with transport term when it is expressed by a graph. The existence of the mean curvature flow with transport term was proved by Liu, Sato, and Tonegawa [19] by using geometric measure theory. We give a proof of the gradient estimates and the short time existence for the mean curvature flow with transport term by applying the backward heat kernel.