Abstract
The authors consider a model of ferromagnetic material subject to an electric current, and prove the local in time existence of very regular solutions for this model in the scale of Hk spaces. In particular, they describe in detail the compatibility conditions at the boundary for the initial data.
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Alouges, F. and Soyeur, A., On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness, Nonlinear Anal., 18(11), (1992), 1071–1084.
Aubin, T., Un théorème de compacité, C. R. Acad. Sci. Paris, 256, (1963), 5042–5044.
Bonithon, G., Landau-Lifschitz-Gilbert equation with applied electric current, Discrete Contin. Dyn. Syst. 2007, Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference, suppl., 138–144.
Boyer, F. and Fabrie, P., Eléments d’analyse pour l’étude de quelques modèles d’écoulements de fluides visqueux incompressibles, Mathématiques & Applications, 52, Springer-Verlag, Berlin, 2006.
Brown, W. F., Micromagnetics, Wiley, New York, 1963.
Carbou, G. and Fabrie, P., Time average in micromagnetism, J. Differential Equations, 147(2), (1998), 383–409.
Carbou, G. and Fabrie, P., Regular solutions for Landau-Lifschitz equations in a bounded domain, Differential Integral Equations, 14, (2001), 213–229.
Carbou, G., Fabrie, P. and Guès, O., On the ferromagnetism equations in the non static case, Commun. Pure Appl. Anal., 3(3), (2004), 367–393.
Foias, G. and Temam, R., Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation, An. Sc. Norm. Super. Pisa IV, 5, (1978), 29–63.
Ladyzhenskaya, O. A., The boundary value problem of mathematical physics, Applied Math. Sciences, 49, Springer-Verlag, New York, 1985.
Landau, L. and Lifschitz, E., Electrodynamique des milieux continues, cours de physique théorique, Tome VIII, Mir (ed.), Moscou, 1969.
Simon, J., Compact sets in the space L p(0, T;B), Ann. Mat. Pura Appl., 146(4), (1987), 65–96.
Thiaville, A., Nakatani, Y., Miltat, J. and Susuki, Y., Micromagnetic understanding of current driven domain wall motion in patterned nanowires, Europhys. Lett., 69(6), (2005), 990–996.
Thiaville, A., Nakatani, Y., Miltat, J. and Vernier, N., Domain wall motion by spin-polarized current: A micromagnetic study, J. Appl. Phys., Part 2, 95(11), (2004), 7049–7051.
Thiaville, A., Garcia, J. M. and Miltat, J., Domain wall dynamics in nanowires, Journal of Magnetism and Magnetic Materials, 242-245, (2002), 1061–1063.
Visintin, A., On Landau Lifschitz equation for ferromagnetism, Japan Journal of Applied Mathematics, 1(2), (1985), 69–84.
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Carbou, G., Jizzini, R. Very Regular Solutions for the Landau-Lifschitz Equation with Electric Current. Chin. Ann. Math. Ser. B 39, 889–916 (2018). https://doi.org/10.1007/s11401-018-0103-7
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DOI: https://doi.org/10.1007/s11401-018-0103-7