Harpes, Paul2021-04-262021-04-262004-07-05Harpes, P. (2004). Partial compactness for the 2-D Landau-Lifshitz flow. <i>Electronic Journal of Differential Equations, 2004</i>(90), pp. 1-24.1072-6691https://hdl.handle.net/10877/13444Uniform local C∞-bounds for Ginzburg-Landau type approximations for the Landau-Lifshitz flow on planar domains are proven. They hold outside an energy-concentration set of locally finite parabolic Hausdorffdimension 2, which has finite times-slices. The approximations subconverge to a global weak solution of the Landau-Lifshitz flow, which is smooth away from the energy concentration set. The same results hold for sequences of global smooth solutions of the 2-d Landau-Lifshitz flow.Text24 pages1 file (.pdf)enAttribution 4.0 InternationalPartial compactnessPartial regularityLandau-Lifshitz flowA priori estimatesHarmonic map flowNon-linear parabolicStruwe-solutionApproximationsArticle