Geodesic
Partial compactness for the 2-D Landau-Lifshitz flow
Electronic journal of differential equations, Tome 2004 (2004)
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__a71,
     author = {Harpes,  Paul},
     title = {Partial compactness for the {2-D} {Landau-Lifshitz} flow},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1058.35078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a71/}
}
TY  - JOUR
AU  - Harpes,  Paul
TI  - Partial compactness for the 2-D Landau-Lifshitz flow
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a71/
LA  - en
ID  - EJDE_2004__2004__a71
ER  - 
%0 Journal Article
%A Harpes,  Paul
%T Partial compactness for the 2-D Landau-Lifshitz flow
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a71/
%G en
%F EJDE_2004__2004__a71
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__a71/