Electron. J. Diff. Eqns.,
Vol. 2004(2004), No. 90, pp. 124.
Partial compactness for the 2D LandauLifshitz flow
Paul Harpes
Abstract:
Uniform local
bounds
for GinzburgLandau type
approximations for the LandauLifshitz flow on planar domains
are proven. They hold outside an energyconcentration set of
locally finite parabolic Hausdorffdimension 2, which has
finite timesslices. The approximations subconverge to a global
weak solution of the LandauLifshitz flow, which is smooth away
from the energy concentration set. The same results hold for
sequences of global smooth solutions of the 2d LandauLifshitz 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;
LandauLifshitz flow; a priori estimates; harmonic map flow;
nonlinear parabolic; Struwesolution; approximations.
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Paul Harpes
ETH Zurich
Ramistrasse 101, 8092 Zurich, Switzerland
email: pharpes@math.ethz.ch 
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