Weak–strong uniqueness for the Landau–Lifshitz–Gilbert equation in micromagnetics
Tài liệu tham khảo
Alouges, 1992, On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness, Nonlinear Anal., 18, 1071, 10.1016/0362-546X(92)90196-L
Carbou, 2001, Regular solutions for Landau-Lifshitz equation in a bounded domain, Differential Integral Equations, 14, 213, 10.57262/die/1356123353
Carbou, 2001, Regular solutions for Landau-Lifshitz equation in R3, Commun. Appl. Anal., 5, 17
Melcher, 2012, Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions, Indiana Univ. Math. J., 61, 1175, 10.1512/iumj.2012.61.4717
Feischl, 2017, Existence of regular solutions of the Landau–Lifshitz–Gilbert equation in 3D with natural boundary conditions, SIAM J. Math. Anal., 49, 4470, 10.1137/16M1103427
Prohl, 2001
Constantin, 1988
Ożański, 2018, Leray’s fundamental work on the navier-Stokes equations: a modern review of “sur le mouvement d’un liquide visqueux emplissant l’espace”, vol. 452, 113
Dumas, 2014, On the weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto–Hydrodynamic equations, Comm. Math. Phys., 330, 1179, 10.1007/s00220-014-1924-1
Kalousek, 2019
Alouges, 2008, A new finite element scheme for Landau-Lifchitz equations, Discrete Contin. Dyn. Syst. Ser. S, 1, 187
Bartels, 2006, Convergence of an implicit finite element method for the Landau-Lifshitz-gilbert equation, SIAM J. Numer. Anal., 44, 1405, 10.1137/050631070
Hrkac, 2019, Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics, Adv. Comput. Math., 45, 1329, 10.1007/s10444-019-09667-z
Abert, 2014, Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator, Comput. Math. Appl., 68, 639, 10.1016/j.camwa.2014.07.010
Di Fratta, 2019, Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-gilbert equation, IMA J. Numer. Anal., 10.1093/imanum/drz046
Moffatt, 2014, Helicity and singular structures in fluid dynamics, Proc. Natl. Acad. Sci. USA, 111, 3663, 10.1073/pnas.1400277111
Hardt, 1986, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., 105, 547, 10.1007/BF01238933
Melcher, 2014, Chiral skyrmions in the plane, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470, 10.1098/rspa.2014.0394
Praetorius, 2004, Analysis of the operator Δ−1div arising in magnetic models, Z. Anal. Anwend., 23, 589, 10.4171/ZAA/1212
Di Fratta, 2019
Carbou, 2007, Couche limite dans un modèle de ferromagnétisme, Commun. Partial Differential Equations, 27, 1467
Leoni, 2017
Evans, 2010
Cimrák, 2007, Existence, regularity and local uniqueness of the solutions to the Maxwell–Landau–Lifshitz system in three dimensions, J. Math. Anal. Appl., 329, 1080, 10.1016/j.jmaa.2006.06.080