Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 90, pp. 1-24.

Title: Partial compactness for  the 2-D Landau-Lifshitz flow

Author: Paul Harpes (ETH Zurich, Switzerland)
 
Abstract: 
  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.
 
Submitted September 11, 2003. Published July 5, 2004.
Math Subject Classifications: 35B65, 35B45, 35D05, 35D10, 35K45, 35K50, 35K55.
Key Words: Partial compactness; partial regularity;  
           Landau-Lifshitz  flow; a priori  estimates; harmonic map flow; 
	   non-linear parabolic; Struwe-solution; approximations.