Electron. J. Diff. Eqns., Vol. 2004(2004), No. 90, pp. 1-24.

Partial compactness for the 2-D Landau-Lifshitz flow

Paul Harpes

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.

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Paul Harpes
ETH Zurich
Ramistrasse 101, 8092 Zurich, Switzerland
email: pharpes@math.ethz.ch

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