  We show uniqueness of classical solutions of the normalised two-dimensional
Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions
satisfying (essentially) only a uniform bound for the Liouville energy and a
natural space-time $L^2$-bound for the time derivative of the solution. The
result is surprising when compared with results for the harmonic map heat flow,
where non-uniqueness through reverse bubbling may occur.
