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

2021/04/08 by Shinya Okabe, Okabe, Shinya, Glen Wheeler +1 · 2 citations
Mathematics · #53A04 #53E40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.03570

openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 → ∞.

Cited by

• Obstacle problems for the elastic flow and related topics
• Stability of flat-core pinned p-elasticae

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