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Mathematics

D-Index
55
Citations
8735
World Ranking
801
National Ranking
387

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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