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Accueil du site > Annuaire > Anciens membres du laboratoire, depuis 2010 > Yvan Martel

Yvan Martel

Professeur

Equipe : Analyse et Equations aux dérivées partielles

Professeur à l’Université de Versailles St-Quentin en détachement auprès de l’Ecole Polytechnique
Membre junior de l’Institut Universitaire de France (2008-2012)

Actuellement Professeur à l’Ecole Polytechnique

Thèmes de recherche

My research activity is currently mainly focused on

  • The asymptotic stability of multi-soliton solutions of nonlinear dispersive equations.
  • The study of the collision of solitons for nonlinear dispersive equations in the nonintegrable case, in collaboration with Frank Merle.

Publications récentes

Y. Martel, F. Merle, P. Raphael, Blow up for the critical gKdV equation I : dynamics near the soliton, arXiv:1204.4625

Y. Martel, F. Merle, P. Raphael, Blow up for the critical gKdV equation II : minimal mass dynamics, arXiv:1204.4624

Y. Martel, F. Merle, P. Raphael, Blow up for the critical gKdV equation III : exotic regimes, arXiv

C. E. Kenig, Y. Martel et L. Robbiano, Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 6, 853-887 (2011).

Y. Martel et F. Merle, Description of two soliton collision for the quartic gKdV equation, Ann. Math. (2) 174, No. 2, 757-857 (2011)

Y. Martel et F. Merle, Inelastic interaction of nearly equal solitons for the quartic gKdV equation, Invent. Math. 183 (2011), no. 3, 563–648,

Y. Martel et F. Merle, Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 2, 287-317 (2011).

R. Côte, Y. Martel, F. Merle, Construction of multi-soliton solutions for the L2 - supercritical gKdV and NLS equations, Rev. Mat. Iberoamericana Volume 27, Number 1 (2011), 273-302.

Y. Martel et F. Merle, Inelastic interaction of nearly equal solitons for the BBM equation, Discrete Contin. Dyn. Syst. 27 (2010), no. 2, 487–532.

Y. Martel, F. Merle et T. Mizumachi, Description of the inelastic collision of two solitary waves for the BBM equation, Arch. Ration. Mech. Anal. 196 (2010), no. 2, 517–574.

J. Krieger, Y. Martel et P. Raphaël, Two-soliton solutions to the three-dimensional gravitational Hartree equation, Communications on Pure and Applied Mathematics, 62 (2009) 1501-1550.

Y. Martel et F. Merle, Stability of two soliton collision for nonintegrable gKdV equations, Communications in Mathematical Physics 286 (2009), 39–79.

C.E. Kenig et Y. Martel, Asymptotic stability of solitons for the Benjamin-Ono equation, Revista Matematica Iberoamericana 25 (2009), 909–970.