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D-Index & Metrics

Mathematics

D-Index
38
Citations
5295
World Ranking
2379
National Ranking
143

Pierre Raphaël publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Pierre Raphaël sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 78 publications — 3rd percentile

3% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Pierre Raphaël D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Pierre Raphaël sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 38 D-Index — 37th percentile

37% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

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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