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.