The p-elastic flow for planar closed curves with constant parametrization

Abstract

In this paper, we consider the L2-gradient flow for the modified p-elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prove the existence of global-in-time weak solutions with p≥2 for initial curves in the energy space via minimizing movements. Moreover, we prove the existence of unique global-in-time solutions to the flow with p=2 and obtain their subconvergence to an elastica as t→∞.