Curve-shortening flow of open, elastic curves in ${\mathbb{R}}^2$ with repelling endpoints: A minimizing movement approach

Abstract

We study an $L^2$-type gradient flow of an immersed elastic curve in ${\mathbb{R}}^2$ whose endpoints repel each other via a Coulomb potential. By De Giorgi's minimizing movements scheme we prove long-time existence of the flow. The work is complemented by several numerical experiments.

References in corpus (2)

• Fractional vortices and composite domain walls in flat nanomagnets
• A Ginzburg-Landau model with topologically induced free discontinuities