@Article{JPDE-20-11,
author = {Yunhua Ye  and Shijin Ding },
title = {Partial Regularity for the 2-dimensional Weighted Landau-Lifshitz Flow},
journal = {Journal of Partial Differential Equations},
year = {2007},
volume = {20},
number = {1},
pages = {11--29},
abstract = {<p>We consider the partial regularity of weak solutions to the weighted Landau-Lifshitz flow on a 2-dimensional bounded smooth domain by Ginzburg-Landau type approximation. Under the energy smallness condition, we prove the uniform local C^∞ bounds for the approaching solutions. This shows that the approximating solutions are locally uniformly bounded in C^∞(Reg({u_∈})∩(\overline{\Omega}×R^+)) which guarantee the smooth convergence in these points. Energy estimates for the approximating equations are used to prove that the singularity set has locally finite two-dimensional parabolic Hausdorff measure and has at most finite points at each fixed time. From the uniform boundedness of approximating solutions in C^∞(Reg({u_∈})∩(\overline{\Omega}×R^+)), we then extract a subsequence converging to a global weak solution to the weighted Landau-Lifshitz flow which is in fact regular away from finitely many points.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5290.html}
}