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Mathematics

D-Index
38
Citations
5295
World Ranking
2378
National Ranking
143

Overview

Pierre Raphaël is affiliated with Université Côte d'Azur in France. Their research intersects various subfields within Mathematics and Physics and Astronomy, focusing notably on advanced problems in mathematical physics.

The main fields of study for Raphaël include:

  • Mathematics
  • Physics and Astronomy

Key subfields of study in their work are:

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Computational Mechanics

The topics covered by Raphaël's research span:

  • Advanced Mathematical Physics Problems
  • Navier-Stokes equation solutions
  • Nonlinear Waves and Solitons
  • Nonlinear Photonic Systems
  • Photonic and Optical Devices
  • Fluid Dynamics and Turbulent Flows
  • Aquatic and Environmental Studies

Raphaël has contributed to several recent publications, including:

  • On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles (2022) published in Annals of Mathematics
  • On the implosion of a compressible fluid II: Singularity formation (2022) published in Annals of Mathematics
  • On blow up for the energy super critical defocusing nonlinear Schrödinger equations (2021) published in Inventiones mathematicae
  • On weakly turbulent solutions to the perturbed linear harmonic oscillator (2023) published in American Journal of Mathematics
  • On Traveling Waves of the Nonlinear Schrödinger Equation Escaping a Potential Well (2020) published in Annales Henri Poincaré

Their frequent coauthors include:

  • Erwan Faou
  • Frank Merle
  • Igor Rodnianski
  • Jérémie Szeftel
  • Yoann Le Hénaff

Raphaël's work has appeared repeatedly in these publication venues:

  • Annals of Mathematics
  • Annales Henri Poincaré
  • Inventiones mathematicae
  • American Journal of Mathematics
  • arXiv (Cornell University)

Best Publications

  • The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

    Frank Merle;Pierre Raphaël

  • Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation

    Frank Merle;Pierre Raphael

  • On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation

    Frank Merle;Frank Merle;Pierre Raphael

  • Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

    Pierre Raphaël;Igor Rodnianski

  • Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

    Frank Merle;Frank Merle;Pierre Raphael

  • Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS

    Pierre Raphaël;Jeremie Szeftel

  • Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem

    Frank Merle;Pierre Raphaël;Igor Rodnianski

  • Nondispersive solutions to the L 2 -critical Half-Wave Equation

    Joachim Krieger;Enno Lenzmann;Pierre Raphaël

  • 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 of the log-log bound for blow up solutions to the critical non linear Schrödinger equation

    Pierre Raphael

  • Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow

    Pierre Raphaël;Remi Schweyer

  • On the stability of critical chemotactic aggregation

    Pierre Raphaël;Rémi Schweyer

  • Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation

    Matthieu Hillairet;Pierre Raphaël

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

    Joachim Krieger;Yvan Martel;Pierre Raphael

  • Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation

    Gadi Fibich;Frank Merle;Pierre Raphaël

  • Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions

    Charles Collot;Frank Merle;Frank Merle;Pierre Raphaël

  • The instability of Bourgain-Wang solutions for the L2 critical NLS

    Frank Merle;Pierre Raphaël;Jeremie Szeftel

  • Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation

    Pierre Raphaël

  • Nondispersive solutions to the L2-critical half-wave equation

    Joachim Krieger;Enno Lenzmann;Pierre Raphael

  • Blow up of the critical norm for some radial L2 super critical nonlinear Schrödinger equations

    Frank Merle;Pierre Raphäel

Frequent Co-Authors

Frank Merle
Frank Merle CY Cergy Paris University
Yvan Martel
Yvan Martel École Polytechnique
Igor Rodnianski
Igor Rodnianski Princeton University
Kenji Nakanishi
Kenji Nakanishi Kyoto University
James Colliander
James Colliander University of British Columbia
Fabrice Planchon
Fabrice Planchon Sorbonne University

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