Raphaël Côte Professor Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg 7 rue René-Descartes 67084 Strasbourg Cedex, France Email : Office : i407 Phone :   +33 3 68 85 01 44

• I hold a chair funded by the IdEX of the University of Strasbourg.
• I am the head of the Modelisation and Control (MOCO) group.
• I organised with Thomas Duyckaerts and Yannick Privat a conference on Control and Dynamics of PDE, at the IRMA, from October 28th to 31st 2019.

Research

Research themes

• 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.
• Solitons, multi-solitons, breathers, self-similar solutions.
• Micromagnetism, Landau-Lifshitz-Gilbert equation, Néel walls.

Preprints

• Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation.
  With Yvan Martel and Xu Yuan.


• Polynomial growth of high Sobolev norms of solutions to the Zakharov-Kuznetsov equation.
  With Frédéric Valet.


• Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations.
  With Yvan Martel, Xu Yuan and Lifeng Zhao.

Publications

• Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation.
  With Simão Correia and Luis Vega. To appear in Journal de Mathématiques Pures et Appliquées.


• Self-similar dynamics for the modified Korteweg-de Vries equation.
  With Simão Correia and Luis Vega. To appear in International Mathematics Research Notices.


• Multi-travelling waves for the nonlinear Klein-Gordon equation.
  With Yvan Martel. Transactions of the American Mathematical Society. 370 (2018) n^o 10, 7461-7487.


• Profiles for the radial focusing 4D energy-critical wave equation.
  With Carlos E. Kenig, Andrew Lawrie and Wilhelm Schlag. Communications in Mathematical Physics. 357 (2018) n^o 4, 943-1008.


• Limiting motion for the parabolic Ginzburg-Landau equation with infinite energy data.
  With Delphine Côte. Communications in Mathematical Physics. 350 (2017) n^o 2, 507-568.


• Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons.
  With Claudio Muñoz, Didier Pilod and Gideon Simpson. Archive for Rational Mechanics and Analysis. 220 (2016) n^o 2, 639-710.


• On the soliton resolution for equivariant wave maps to the sphere.
  Communications on Pure and Applied Mathematics. 68 (2015), 1946-2004.


• Characterization of large energy solutions of the equivariant wave map problem: II.
  With Carlos E. Kenig, Andrew Lawrie and Wilhelm Schlag. American Journal of Mathematics. 137 (2015) n^o 1, 209-250.


• Characterization of large energy solutions of the equivariant wave map problem: I.
  With Carlos E. Kenig, Andrew Lawrie and Wilhelm Schlag. American Journal of Mathematics. 137 (2015) n^o 1, 139-207.


• A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls.
  With Radu Ignat and Evelyne Miot. Journal of Fixed Point Theory and Applications. 15 (2014), The Haïm Brezis Festschrift, n^o 1, 241-272.


• Multi-solitons for the nonlinear Klein-Gordon equation.
  With Claudio Muñoz. Forum of Mathematics, Sigma. 2 (2014), e15, 38 pp.


• Energy partition for the linear wave equation.
  With Carlos E. Kenig and Wilhelm Schlag. Mathematische Annalen. 358 (2014), 573-607.


• Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimension.
  With Hatem Zaag. Communications on Pure and Applied Mathematics. 66 (2013) n^o 10, 1541-1581.


• 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) n^o 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) n^o 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), 845-848.


• Construction of solutions to the L²-critical KdV equation with a given asymptotic behaviour.
  Duke Mathematical Journal. 138 (2007) n^o 3, 487-532.


• Construction of solutions to the subcritical gKdV equations with a given asymptotic 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) n^o 2, 163-188.


• Instability of non-constant harmonic maps for the (1+2)-dimensional equivariant wave map system.
  International Mathematics Research Notices. 2005 n^o 57, 3525-3549.

Proceedings

• Around self-similar solutions to the modified Korteweg-de Vries equation.
  Oberwolfach reports. (2019).


• Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation.
  Séminaire Laurent-Schwartz. 2018-2019. Exp. 4, 15 pages. École Polytechnique, Palaiseau (2019).


• Les solitons.
  Gazette des Mathématiciens. 153 (2017), 59-63.


• Asymptotic stability of solitons for the Zahkarov-Kuznetsov equation.
  Oberwolfach reports. 13, no. 2, 1531-1534. (2016).


• Soliton resolution for equivariant wave maps to the sphere.
  Oberwolfach reports. 10, no. 3, 2331-2333. (2013).


• Construction de solutions pour les équations de Korteweg-de Vries généralisées.
  Séminaire: Équations aux Dérivées Partielles. 2006-2007. Exp. 3, 17 pages. École Polytechnique, Palaiseau (2007).


• Solutions to the generalized Korteweg-de Vries equations with a prescribed asymptotic behavior.
  Oberwolfach reports. 4, no. 4, 2637-2639. (2007).

Thesis

• Construction et propriétés de solutions pour des équations dispersives focalisantes.
  PhD thesis.


• Solitons et dispersion.
  Habilitation thesis.

Editorial board

• I am a member of the editorial board of the Cours spécialisés of the French Mathematical Society (SMF).

Collaborators

• Simão Correia
• Delphine Côte
• Radu Ignat
• Carlos E. Kenig
• Andrew Lawrie
• Stefan Le Coz
• Yvan Martel
• Frank Merle
• Evelyne Miot
• Claudio Muñoz
• Didier Pilod
• Wilhelm Schlag
• Gideon Simpson
• Frédéric Valet
• Luis Vega
• Xu Yuan
• Hatem Zaag
• Lifeng Zhao

• Yakine Bahri. PhD defended in july 2016, École polytechnique (co-supervision with Philippe Gravejat).
• Xavier Friederich, since 2018.
• Alexander Semenov, since 2018.
• Frédéric Valet, since 2016.

• Simão Correia (2017-2018).
• Clémentine Courtès (2017-2018).

Teaching

• Integration and Probabilities for the Agrégation (graduate level),
• Techniques of numerical Analysis I (3rd year),
• Techniques of numerical Analysis II (3rd year),
• Calculus (1st year).

  

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Last change: December 2019.