Geodesic
Partial compactness for the 2-D Landau-Lifshitz flow
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35B65, 35B45, 35D05, 35D10, 35K45, 35K50, 35K55
Keywords: partial compactness, partial regularity, Landau-Lifshitz flow, a priori estimates, harmonic map flow, non-linear parabolic, struwe-solution, approximations 
@article{EJDE_2004__2004__a171,
     author = {Harpes, Paul},
     title = {Partial compactness for the {2-D} {Landau-Lifshitz} flow},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a171/}
}
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Harpes, Paul. Partial compactness for the 2-D Landau-Lifshitz flow. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a171/