Finite Time singularity of the Landau-Lifshitz-Gillbert Equation

Landau, 1935, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Physikalische Zeitschrift der Sowjetunion, 8, 153

Chen, 1989, The weak solutions to the evolution problems of harmonic maps, Mathematische Zeitschrift, 201, 69, 10.1007/BF01161995

Struwe, 1988, On the evolution of harmonic maps in higher dimensions, Journal of Differential Geometry, 28, 485, 10.4310/jdg/1214442475

Chen, 1989, Existence and partial regularity results for the heat flow for harmonic maps, Mathematische Zeitschrift, 201, 83, 10.1007/BF01161997

Chen, 1993, Evolution of harmonic maps with Dirichlet boundary conditions, Communications in Analysis and Geometry, 1, 327, 10.4310/CAG.1993.v1.n3.a1

Coron, 1989, Explosion en temps fini pour le flot des applications harmoniques, Comptes Rendus de l'Acadmie des Sciences-Series I-Mathematics, 308, 339

Chen, 1990, Blow-up and global existence for heat flows of harmonic maps, Inventiones Mathematicae, 99, 567, 10.1007/BF01234431

Alouges, 1992, On global weak solutions for Landau-Lifshitz equations: existence and uniqueness, Nonlinear Analysis, 18, 1071, 10.1016/0362-546X(92)90196-L

Chen, 1998, Partial regularity for two dimensional Landau-Lifshitz equations, Acta Mathematica Sinica-English Series, 41, 1043, 10.1360/012011-393

Moser, Max-Planck-Institute for Mathematics in the Sciences 26

Moser, 2005, Partial Regularity for Harmonic Maps and Related Problems, 10.1142/5691

Liu, 2004, Partial regularity for the Landan-Lifshitz system, Calculus of Variations and Partial Differential Equations, 20, 153, 10.1007/s00526-003-0231-z

Feldman, 1994, Partial regularity for harmonic maps of evolution into spheres, Communications in Partial Differential Equations, 19, 761, 10.1080/03605309408821034

Chen, 1995, Partial regularity for weak heat flows into spheres, Communications on Pure and Applied Mathematics, 158, 429, 10.1002/cpa.3160480403

Guo, 1993, The Landau-Lifshitz equation fo the ferromagnetic spin chain and harmonic maps, Calculus of Variations and Partial Differential Equations, 1, 311, 10.1007/BF01191298

Melcher, 2005, Existence of partially regular solutions for Landau-Lifshitz equations in R3, Communications in Partial Differential Equations, 30, 567, 10.1081/PDE-200050122

Wang, 2006, On Landau-Lifshitz equation in dimensions at most four, Indiana University Mathematics Journal, 55, 1615, 10.1512/iumj.2006.55.2810

Bartels, 2005, Numerical approximation of the landau-lifshitz-gilbert equation and finite time blow-up of weak solutions

Pistella, 2002, Numerical Study of the Appearance of Singularities in Ferromagnets, Advances in Mathematical Sciences and Applications, 12, 803

Struwe, 1996, Nonlinear PDE in Differential Geometry, 259

White, 1986, Infima of energy functionals in homotopy classes of mappings, Journal of Differential Geometry, 23, 127, 10.4310/jdg/1214440023

Chang, 1992, Finite-time blow-up of the heat flow of harmonic maps from surfaces, Journal of Differential Geometry, 36, 507, 10.4310/jdg/1214448751

Fefferman, 1972, spaces of several variables, Acta Mathematica, 129, 137, 10.1007/BF02392215

Semmes, 1994, A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Communications in Partial Differential Equations, 19, 277, 10.1080/03605309408821017