On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces (Q2021698)

This paper studies the mean curvature flow of rotationally symmetric closed surfaces by transforming the equation into a degenerate parabolic system with moving boundaries in one space dimension. By the rotational symmetry, the mean curvature flow can be expressed as a one-dimensional singular equation in terms of the radial variable along with singular boundary conditions. By considering the square of its solution, the authors further build a new parabolic system, which does not contain any singular coefficients. Based on this new formulation, the authors obtain the existence and uniqueness of classical solutions in a maximal time interval. The smoothing effect of this equation is also discussed.