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Mathematics

D-Index
36
Citations
6709
World Ranking
2607
National Ranking
155

Overview

Yvan Martel is affiliated with École Polytechnique in France and has contributed extensively to research in physics and mathematics. Their work predominantly focuses on advanced mathematical physics problems and nonlinear systems, with significant attention to nonlinear waves and solitons.

Their main fields of study include:

  • Physics and Astronomy
  • Mathematics

Within these areas, their subfields of study cover:

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Applied Mathematics
  • General Health Professions
  • Atomic and Molecular Physics, and Optics

The primary topics addressed in their research are:

  • Advanced Mathematical Physics Problems
  • Nonlinear Photonic Systems
  • Nonlinear Waves and Solitons
  • Navier-Stokes Equation Solutions
  • Cold Atom Physics and Bose-Einstein Condensates
  • Stochastic Processes and Statistical Mechanics
  • Random Matrices and Applications

Martel's recent published papers illustrate their focus on nonlinear wave equations and soliton dynamics:

  • "Soliton Resolution for Critical Co-rotational Wave Maps and Radial Cubic Wave Equation," 2022, Communications in Mathematical Physics
  • "Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5," 2020, Journal de Mathématiques Pures et Appliquées
  • "Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes," 2021, Journal of the European Mathematical Society
  • "A Sufficient Condition for Asymptotic Stability of Kinks in General (1+1)-Scalar Field Models," 2021, Annals of PDE
  • "Description and Classification of 2-Solitary Waves for Nonlinear Damped Klein-Gordon Equations," 2021, Communications in Mathematical Physics

The venues where Martel frequently publishes include:

  • arXiv (Cornell University)
  • Communications in Mathematical Physics
  • Journal de Mathématiques Pures et Appliquées
  • Journal of the European Mathematical Society
  • Annals of PDE

Collaborations play a notable role in their research. Their frequent co-authors are:

  • Michał Kowalczyk
  • Claudio Muñoz
  • Thomas Duyckaerts
  • Carlos E. Kenig
  • Frank Merle

Best Publications

  • An Introduction to Semilinear Evolution Equations

    Thierry Cazenave;Alain Haraux;Yvan Martel

  • Blow up for $u_t-\Delta u=g(u)$ revisited

    Haïm Brezis;Thierry Cazenave;Yvan Martel;Arthur Ramiandrisoa

  • ASYMPTOTIC N-SOLITON-LIKE SOLUTIONS OF THE SUBCRITICAL AND CRITICAL GENERALIZED KORTEWEG-DE VRIES EQUATIONS

    Yvan Martel

  • Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations

    Yvan Martel;Franck Merle

  • A Liouville theorem for the critical generalized Korteweg de Vries equation

    Yvan Martel;Franck Merle;Franck Merle

  • Stability and Asymptotic Stability for Subcritical gKdV Equations

    Yvan Martel;Frank Merle;Tai-Peng Tsai

  • Asymptotic stability of solitons of the subcritical gKdV equations revisited

    Yvan Martel;Franck Merle

  • Instability of solitons for the critical generalized Korteweg—de Vries equation

    Yvan Martel;Franck Merle

  • Blow up in finite time and dynamics of blow up solutions for the ²–critical generalized KdV equation

    Yvan Martel;Frank Merle

  • Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation

    Yvan Martel;Frank Merle

  • Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations

    Raphaël Côte;Yvan Martel;Frank Merle

  • Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier

    Xavier Cabré;Yvan Martel

  • Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space

    Michał Kowalczyk;Yvan Martel;Claudio Muñoz

  • Multi solitary waves for nonlinear Schrödinger equations

    Yvan Martel;Frank Merle

  • Asymptotic stability of solitons of the gKdV equations with general nonlinearity

    Yvan Martel;Frank Merle

  • Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton

    Yvan Martel;Yvan Martel;Frank Merle;Pierre Raphaël;Pierre Raphaël

  • Stability in H1 of the sum of K solitary waves for some nonlinear Schrödinger equations

    Yvan Martel;Franck Merle;Tai-Peng Tsai

  • Description of two soliton collision for the quartic gKdV equation

    Yvan Martel;Frank Merle

  • Two‐soliton solutions to the three‐dimensional gravitational Hartree equation

    Joachim Krieger;Yvan Martel;Pierre Raphael

  • Weak Eigenfunctions for the Linearization of Extremal Elliptic Problems

    Xavier Cabré;Yvan Martel

  • Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations

    Yvan Martel;Frank Merle;Tai-Peng Tsai

Frequent Co-Authors

Frank Merle
Frank Merle CY Cergy Paris University
Pierre Raphaël
Pierre Raphaël Université Côte d'Azur
Thierry Cazenave
Thierry Cazenave Sorbonne University
Carlos E. Kenig
Carlos E. Kenig University of Chicago
Xavier Cabré
Xavier Cabré Universitat Politècnica de Catalunya
Philippe Souplet
Philippe Souplet Paris 13 University
Haim Brezis
Haim Brezis Rutgers, The State University of New Jersey
Kenji Nakanishi
Kenji Nakanishi Kyoto University

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