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

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 & GE; 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-+ & INFIN;.& COPY; 2023 Elsevier Masson SAS. All rights reserved.

Automated summary

In this paper, we study the L2-gradient flow of the modified p-elastic energy on planar closed curves. We introduce a notion of weak solution for the flow and prove the existence of global-in-time weak solutions for initial curves in the energy space when p ≥ 2 using the method of minimizing movements. Furthermore, we establish the existence of unique global-in-time solutions to the flow when p = 2 and show their subconvergence to an elastica as t tends to infinity.