On the $L^{2}$-flow of elastic curves
Anna Dall'Acqua (Ulm)
Elastic curves are critical points of the elastic energy, that is the integral
of the curvature squared. A natural approach to get to minimisers is to study the associated
steepest descent flow. We study the evolution of open curves satisfying some boundary conditions
and moving in time so that the elastic energy decreases while the length is kept fixed.
We show that, if the initial datum is smooth enough, the solution exists
globally in time and subconverges to a critical point.