The gradient flow of the potential energy on the space of arcs

Wenhui Shi, Dmitry Vorotnikov

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2 Citations (Scopus)


We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of generalized solutions to the corresponding nonlinear evolutionary PDE and their exponential decay to the equilibrium. We also observe that the system admits solutions backwards in time, which leads to non-uniqueness of trajectories.
Original languageEnglish
Article number59
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Issue number2
Publication statusPublished - 1 Apr 2019
Externally publishedYes

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