Uniqueness and bubbling of the 2-dimensional Landau-Lifshitz flow (Q1890020)

The author considers the Landau-Lifshitz flow on a bounded planar domain. Among other results a clarification is provided of a known uniqueness result for the Landau-Lifshitz flow and a proof of the fact that tells how non-uniqueness of extensions of the flow after point singularities is related to backward bubbling. The paper concludes with the \(\varepsilon\)-regularity estimate which implies a partial solution (a compactness result) for sequences of smooth solutions to the Landau-Lifshitz flow with uniformly bounded energy that is defined on a planar domain.