Infinite-time convergence of geometric flows, as even for finite-dimensional gradient flows, is a notoriously subtle problem. The best (or only) bet is to get a Łojasiewicz(-Simon) inequality stating that a power of the gradient dominates the distance to the critical energy value. I'll introduce a Łojasiewicz inequality between the tension field and Dirichlet energy of a map from the 2-sphere to itself, removing the technical restrictions from an estimate of Topping (Annals ‘04). The inequality guarantees convergence of weak solutions of harmonic map flow from $S^2$ to $S^2$ assuming that the body map is nonconstant.