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Existence of partially regular weak solutions to Landau–Lifshitz–Maxwell equations
- Source :
-
Journal of Differential Equations . May2008, Vol. 244 Issue 10, p2448-2472. 25p. - Publication Year :
- 2008
-
Abstract
- Abstract: In this paper, the authors establish the existence of partially regular weak solutions to the Landau–Lifshitz equations coupling with static Maxwell systems in 3 dimensions by Ginzburg–Landau approximation. It is proved that the Hausdorff measure of the singular set is locally finite. This extends the similar results of Ding and Guo [S. Ding, B. Guo, Hausdorff measure of the singular set of Landau–Lifshitz equations with a nonlocal term, Comm. Math. Phys. 250 (1) (2004) 95–117] from the stationary solutions to weak solutions and the results of Wang [C. Wang, On Landau–Lifshitz equations in dimensions at most four, Indiana Univ. Math. J. 55 (5) (2006) 1615–1644] from Landau–Lifshitz equations to Landau–Lifshitz–Maxwell equations. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 244
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 31564509
- Full Text :
- https://doi.org/10.1016/j.jde.2008.02.029