Partial regularity for two dimensional Landau-Lifshitz equations. (English) Zbl 0906.35025
It is considered an initial value problem for the two-dimensional Landau-Lifshitz equation
\[
\partial_t u=\alpha u\times \partial_t u+\beta \Delta_Mu+\beta | du|^2 u
\]
on \(M\times \mathbb{R}^+\), where \(M\) is a compact two dimensional Riemannian manifold without boundary. It is proved existence and uniqueness of a weak solution which is smooth with the exception of at most finitely many points.
Reviewer: Lubomira Softova (Sofia)
MSC:
| 35D10 | Regularity of generalized solutions of PDE (MSC2000) |
| 35K55 | Nonlinear parabolic equations |
| 35Q80 | Applications of PDE in areas other than physics (MSC2000) |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
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