Smoothness of Local Solutions for the 4th-Order Elastic Flow of Inextensible Plane Curves Smoothness of Local Solutions for the 4th-Order Elastic Flow of Inextensible Plane Curves

2016

Chang, Yu-Wei
Abstract

In this paper we establish the smooth short time existence of the inextensible elastic flow, provided that our initial plane curves is $C^{3+\alpha}$. We consider two cases of initial plane curves: closed curves and open curves with hinged end. The inextensible elastic flow of such plane curves correspond to semi-linear fourth-order parabolic equations.