\(\mathcal{F}\)-stability of self-similar solutions to harmonic map heat flow (Q690647)

The author is interested in the notion of generic singularities for the harmonic map heat flow. By introducing the \(\mathcal{F}\)-functional and entropy for harmonic map, and \(\mathcal{F}\)-stability for weakly self-similar solutions, the author shows that the critical points of the \(\mathcal{F}\)-functional are exactly the same as the weakly self-similar solutions to the harmonic map heat flow, and the \(\mathcal{F}\)-stability can be characterized by the semi-positive definiteness of the Jacobi operator acting on a subspace of variation fields.