%0 Journal Article
%T Partial compactness for the 2-D Landau-Lifshitz flow
%A Paul Harpes
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X Uniform local $C^infty$-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 Hausdorff-dimension 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.
%K Partial compactness
%K partial regularity
%K Landau-Lifshitz flow
%K a priori estimates
%K harmonic map flow
%K non-linear parabolic
%K Struwe-solution
%K approximations.
%U http://ejde.math.txstate.edu/Volumes/2004/90/abstr.html