World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
55
Citations
8735
World Ranking
801
National Ranking
388

Kevin Zumbrun 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 Kevin Zumbrun 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: 215 publications — 67th percentile

67% of scientists in this discipline score the same or lower.

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

Kevin Zumbrun 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 Kevin Zumbrun 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: 55 D-Index — 79th percentile

79% of scientists in this discipline score the same or lower.

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

Research.com Recognitions

  • 2017 - SIAM Fellow For his contributions in traveling wave stability and his exceptional mentoring of graduate students and post-doctoral researchers.
  • 2014 - Fellow of the American Mathematical Society For contributions to continuum mechanics, shock, and boundary layer theory.

Overview

Kevin Zumbrun is affiliated with Indiana University in the United States and has contributed extensively to the fields of mathematics and engineering, with a strong focus on applied mathematics, computational mechanics, and mathematical physics. Their research spans several main topics, including Navier-Stokes equation solutions, advanced mathematical physics problems, and stability and controllability of differential equations.

Their work also covers areas related to computational fluid dynamics and aerodynamics, gas dynamics and kinetic theory, fluid dynamics and turbulent flows, as well as nonlinear dynamics and pattern formation.

Kevin Zumbrun's frequent co-authors include:

  • Zhao Yang
  • Aric Wheeler
  • L. Miguel Rodrigues
  • Alim Sukhtayev
  • Yang Zhao

They have contributed to a range of prominent publication venues, including:

  • arXiv (Cornell University)
  • UNC Libraries
  • Physica D Nonlinear Phenomena
  • Water Waves
  • Annales de l Institut Henri Poincaré C Analyse Non Linéaire

Notable recent papers by Kevin Zumbrun include:

  • Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato-Lefever waves, 2023, Annales de l Institut Henri Poincaré C Analyse Non Linéaire
  • Convective-Wave Solutions of the Richard-Gavrilyuk Model for Inclined Shallow-Water Flow, 2023, Water Waves
  • Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow, 2024, Archive for Rational Mechanics and Analysis
  • Spectral stability of hydraulic shock profiles, 2020, Physica D Nonlinear Phenomena
  • Convective Turing Bifurcation, 2021, arXiv (Cornell University)

The scholar's work has been recognized through awards such as being named a SIAM Fellow in 2017 for contributions related to traveling wave stability and mentoring. Earlier, in 2014, they were designated as a Fellow of the American Mathematical Society for contributions to continuum mechanics, shock, and boundary layer theory.

Best Publications

  • The gap lemma and geometric criteria for instability of viscous shock profiles

    Robert A. Gardner;Kevin Zumbrun

  • Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow

    David Hoff;Kevin Zumbrun

  • Pointwise Semigroup Methods and Stability of Viscous Shock Waves

    Kevin Zumbrun;Peter Howard

  • Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves

    David Hoff;Kevin Zumbrun

  • Multidimensional Stability of Planar Viscous Shock Waves

    Kevin Zumbrun

  • Viscous and inviscid stability of multidimensional planar shock fronts

    K. Zumbrun;D. Serre

  • Connectivity of Phase Boundaries in Strictly Convex Domains

    Peter Sternberg;Kevin Zumbrun

  • Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems

    Guy Métivier;Kevin R. Zumbrun

  • Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations

    Kevin Zumbrun;Helge Kristian Jenssen;Gregory Lyng

  • Analytically varying eigenvectors and the stability of viscous shock waves

    Leon Brin;Kevin Zumbrun

  • Pointwise Green Function Bounds for Shock Profiles of Systems with Real Viscosity

    Corrado Mascia;Kevin Zumbrun

  • A POINCARE INEQUALITY WITH APPLICATIONS TO VOLUME-CONSTRAINED AREA-MINIMIZING SURFACES

    Kevin Zumbrun;Peter Sternberg

  • An efficient shooting algorithm for Evans function calculations in large systems

    Jeffrey Humpherys;Kevin Zumbrun

  • Pointwise Green's function bounds and stability of relaxation shocks

    Corrado Mascia;Kevin Zumbrun

  • Navier–Stokes regularization of multidimensional Euler shocks

    C. M. I. Olivier Guès;Guy Métivier;Mark Williams;Kevin Zumbrun

  • On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint

    Peter Sternberg;Kevin Zumbrun

  • Stability of Large-Amplitude Viscous Shock Profiles of Hyperbolic-Parabolic Systems

    Corrado Mascia;Kevin Zumbrun

  • An Evans function approach to spectral stability of small-amplitude shock profiles

    Ramón G. Plaza;Kevin Zumbrun

  • Stability of rarefaction waves in viscous media

    Anders Szepessy;Anders Szepessy;Kevin Zumbrun;Kevin Zumbrun

  • Boundary Layer Stability¶in Real Vanishing Viscosity Limit

    Denis Serre;Kevin Zumbrun

  • Hyperbolic boundary value problems for symmetric systems with variable multiplicities

    Guy Métivier;Kevin Zumbrun

  • Advances in the Theory of Shock Waves

    Tai-Ping Liu;Guy Métivier;Joel Smoller;Blake Temple

Frequent Co-Authors

Guy Métivier
Guy Métivier University of Bordeaux
Denis Serre
Denis Serre École Normale Supérieure de Lyon
Peter Sternberg
Peter Sternberg Indiana University
Björn Sandstede
Björn Sandstede Brown University
Russell Lyons
Russell Lyons Indiana University
David Hoff
David Hoff Indiana University
Tai-Ping Liu
Tai-Ping Liu Stanford University
Arnd Scheel
Arnd Scheel University of Minnesota
Fritz Gesztesy
Fritz Gesztesy Baylor University
Andrea L. Bertozzi
Andrea L. Bertozzi University of California, Los Angeles

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