Partial compactness for the 2-D Landau-Lifshitz flow
Date
2004-07-05
Authors
Harpes, Paul
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Uniform local C∞-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 Hausdorffdimension 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.
Description
Keywords
Partial compactness, Partial regularity, Landau-Lifshitz flow, A priori estimates, Harmonic map flow, Non-linear parabolic, Struwe-solution, Approximations
Citation
Harpes, P. (2004). Partial compactness for the 2-D Landau-Lifshitz flow. <i>Electronic Journal of Differential Equations, 2004</i>(90), pp. 1-24.
Rights
Attribution 4.0 International