Raphaël Côte CNRS Research fellow Centre de Mathématiques Laurent Schwartz UMR 7640 École Polytechnique 91128 Palaiseau Cedex - France Email: Office: 10 07 Phone:   +33 1 69 33 49 78 Fax:   +33 1 69 33 49 49

Research

Research interests

• Non-linear evolution PDEs.
• Dynamics, stability, blow-up, asymptotic behaviour and classification of PDEs.
• Wave equations, generalized Korteweg-de Vries equations, non-linear Schrödinger equations, dispersive equations.
• Micromagnetism, Landau-Lifshitz-Gilbert equation, Néel walls.

Preprints

• Multi-solitons for the nonlinear Klein-Gordon equation.
  With Claudio Muñoz.


• Characterization of large energy solutions of the equivariant wave map problem: II.
  With Carlos E. Kenig, Andrew Lawrie and Wilhelm Schlag.


• Characterization of large energy solutions of the equivariant wave map problem: I.
  With Carlos E. Kenig, Andrew Lawrie and Wilhelm Schlag.


• Energy partition for the linear wave equation.
  With Carlos E. Kenig and Wilhelm Schlag.

Publications

• Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimension.
  With Hatem Zaag. To appear in Communications on Pure and Applied Mathematics.


• High speed excited multi-solitons in nonlinear Schrödinger equations.
  With Stefan Le Coz. Journal de Mathématiques Pures et Appliquées 96 (2011), 135-166.


• N-solitons for the L²-supercritical generalized Korteweg-de Vries and non-linear Schrödinger equations.
  With Yvan Martel and Frank Merle. Revista Mathematica Iberoamericana 27 (2011), no. 1, 273-302.


• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system.
  With Carlos E. Kenig and Frank Merle. Communications in Mathematical Physics 284 (2008), no. 1, 203-225.


• Scaling-sharp dispersive estimates for the Korteweg-de Vries group.
  With Luis Vega. Comptes Rendus Mathématiques. Académie des Sciences. Paris 346 (2008), no. 15-16, 845-848.


• Construction of solutions to the L²-critical KdV equation with a given asymptotic behaviour.
  Duke Mathematical Journal, 138 (2007), no. 3, 487-532.


• Construction of solutions to the subcritical gKdV equations with a given asymptotical behaviour.
  Journal of Functional Analysis, 241 (2006), 143-211.


• Large data wave operator for the generalized Korteweg-de Vries equations.
  Differential and Integral Equations, 19 (2006), no. 2, 163-188.


• Instability of non-constant harmonic maps for the (1+2)-dimensional equivariant wave map system.
  International Mathematics Research Notices, 2005, no. 57, 3525-3549.

Proceedings

• Construction de solutions pour les équations de Korteweg-de Vries généralisées.
  Séminaire: Équations aux Dérivées Partielles. 2006-2007, Exp. No. III, 17 p., École Polytechnique, Palaiseau, 2007.

PhD

• Construction and propriéties of solutions dispersive focusing equations. Université de Cergy-Pontoise, 2006.

Teaching

• Problem sessions for the class MAT431:
  Differential equations and dynamical systems (Raphaël Krikorian)
  Distributions, Fourier and Partial Differential Equations (François Golse)

Back to the homepage of the CMLS

Last modification: March 2013.