M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Government Printing Oce, vol.55, 1964.

F. Alouges and A. Soyeur, On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness, Nonlinear Anal, vol.18, issue.11, p.10711084, 1992.

J. M. Arrieta, A. Rodriguez-bernal, J. W. Cholewa, and T. Dlotko, Linear parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci, vol.14, issue.2, p.253293, 2004.

V. Banica and L. Vega, On the Dirac delta as initial condition for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.25, issue.4, p.697711, 2008.

V. Banica and L. Vega, On the stability of a singular vortex dynamics, Comm. Math. Phys, vol.286, issue.2, p.593627, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00255836

V. Banica and L. Vega, Scattering for 1D cubic NLS and singular vortex dynamics, J. Eur. Math. Soc, vol.14, issue.1, p.209253, 2012.

V. Banica and L. Vega, Stability of the self-similar dynamics of a vortex lament, Arch. Ration. Mech. Anal, vol.210, issue.3, p.673712, 2013.

P. Biernat and P. Bizo«, Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat ow for harmonic maps between spheres, Nonlinearity, vol.24, issue.8, p.22112228, 2011.

H. Brezis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl, vol.62, issue.9, p.7397, 1983.

H. Brezis and L. Nirenberg, Degree theory and BMO. I. Compact manifolds without boundaries, Selecta Math. (N.S.), vol.1, issue.2, p.197263, 1995.

J. Coron, Nonuniqueness for the heat ow of harmonic maps, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.7, issue.4, p.335344, 1990.

M. Daniel and M. Lakshmanan, Perturbation of solitons in the classical continuum isotropic Heisenberg spin system, Physica A: Statistical Mechanics and its Applications, vol.120, issue.1, pp.125-152, 1983.

S. Ding and C. Wang, Finite time singularity of the Landau-Lifshitz-Gilbert equation, Art. ID rnm012, vol.25, 2007.

P. Germain, N. Pavlovi¢, and G. Stalani, Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO ?1, Art. ID rnm087, p.35, 2007.

P. Germain and M. Rupin, Selfsimilar expanders of the harmonic map ow, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.28, issue.5, p.743773, 2011.

T. L. Gilbert, A lagrangian formulation of the gyromagnetic equation of the magnetization eld, Phys. Rev, vol.100, p.1243, 1955.

S. Gutiérrez and A. De-laire, Self-similar solutions of the one-dimensional LandauLifshitz Gilbert equation, Nonlinearity, vol.28, issue.5, p.1307, 2015.

S. Gutiérrez, J. Rivas, and L. Vega, Formation of singularities and self-similar vortex motion under the localized induction approximation, Comm. Partial Dierential Equations, vol.28, issue.5-6, p.927968, 2003.

H. Hasimoto, A soliton on a vortex lament, J. Fluid Mech, vol.51, issue.3, p.477485, 1972.
DOI : 10.1017/s0022112072002307

L. Hörmander, Lectures on nonlinear hyperbolic dierential equations, of Mathématiques & Applications (Berlin), vol.26

. Springer-verlag, , 1997.

C. E. Kenig, G. Ponce, and L. Vega, On the ill-posedness of some canonical dispersive equations, Duke Math. J, vol.106, issue.3, p.617633, 2001.

H. Koch and T. Lamm, Geometric ows with rough initial data, Asian J. Math, vol.16, issue.2, pp.209-235, 2012.
DOI : 10.4310/ajm.2012.v16.n2.a3

URL : http://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2012/0016/0002/AJM-2012-0016-0002-a003.pdf

H. Koch and D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math, vol.157, issue.1, p.2235, 2001.

O. Ladyzhenskaya, V. Solonnikov, and N. , Ural'tseva. Linear and quasi-linear equations of parabolic type, Amer. Math. Soc., Transl. Math. Monographs. Providence, R.I, 1968.

M. Lakshmanan and K. Nakamura, Landau-Lifshitz equation of ferromagnetism: Exact treatment of the Gilbert damping, Phys. Rev. Lett, vol.53, p.24972499, 1984.

L. Landau and E. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z. Sowjetunion, vol.8, p.153169, 1935.

P. G. Lemarié-rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/CRC Research Notes in Mathematics, vol.431, 2002.

G. M. Lieberman, Second order parabolic dierential equations, 1996.

J. Lin, Uniqueness of harmonic map heat ows and liquid crystal ows, Discrete Contin. Dyn. Syst, vol.33, issue.2, p.739755, 2013.

J. Lin, B. Lai, and C. Wang, Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces, Calc. Var. Partial Dierential Equations, vol.54, issue.1, p.665692, 2015.

C. Melcher, Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions, Indiana Univ. Math. J, vol.61, issue.3, p.11751200, 2012.

H. Miura and O. Sawada, On the regularizing rate estimates of Koch-Tataru's solution to the Navier-Stokes equations, Asymptot. Anal, vol.49, issue.1-2, p.115, 2006.

P. Quittner and P. Souplet, Birkhäuser Advanced Texts: Basler Lehrbücher

, Blow-up, global existence and steady states, 2007.

E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol.43, 1993.

C. Wang, Well-posedness for the heat ow of harmonic maps and the liquid crystal ow with rough initial data, Arch. Ration. Mech. Anal, vol.200, issue.1, p.119, 2011.

D. Wei, Micromagnetics and Recording Materials. SpringerBriefs in Applied Sciences and Technology, 2012.
DOI : 10.1007/978-3-642-28577-6