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D-Index & Metrics

Mathematics

D-Index
41
Citations
6524
World Ranking
1926
National Ranking
823

Research.com Recognitions

  • 2020 - Fellow of the American Mathematical Society For contributions to nonlinear partial differential equations, fluid dynamics, and free-boundary problems.
  • 2000 - Fellow of Alfred P. Sloan Foundation

Overview

Steve Shkoller is a researcher affiliated with the University of California, Davis in the United States. Their research primarily spans the fields of Mathematics and Engineering, with a strong focus on Applied Mathematics and Computational Mechanics. Their work also touches on Mathematical Physics, Astronomy and Astrophysics, and Geometry and Topology as subfields of study.

The main topics of Steve Shkoller's research include:

  • Navier-Stokes equation solutions
  • Computational Fluid Dynamics and Aerodynamics
  • Advanced Mathematical Physics Problems
  • Cosmology and Gravitation Theories
  • Gas Dynamics and Kinetic Theory
  • Geometric Analysis and Curvature Flows
  • Fluid Dynamics and Turbulent Flows

Their recent publications highlight work on the formation and behavior of shocks and fluid dynamics phenomena in compressible Euler equations, reflecting the specialized mathematical analysis they conduct. Some notable papers include:

  • "Formation of Shocks for 2D Isentropic Compressible Euler," 2020, Communications on Pure and Applied Mathematics
  • "Shock Formation and Vorticity Creation for 3d Euler," 2022, Communications on Pure and Applied Mathematics
  • "Simultaneous Development of Shocks and Cusps for 2D Euler with Azimuthal Symmetry from Smooth Data," 2022, Annals of PDE
  • "Formation of Point Shocks for 3D Compressible Euler," 2022, Communications on Pure and Applied Mathematics
  • "The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions," 2024, Inventiones mathematicae

Shkoller often collaborates with other researchers in their field. Frequent coauthors include Vlad Vicol, Tristan Buckmaster, Isaac Neal, Theodore D. Drivas, and Raaghav Ramani.

Their research contributions have been published in venues such as arXiv (Cornell University), Communications on Pure and Applied Mathematics, Annals of PDE, Inventiones mathematicae, and the Journal of Computational Physics. ArXiv is the most frequent publishing platform used, followed by Communications on Pure and Applied Mathematics.

Steve Shkoller's work has been recognized through awards including being named a Fellow of the American Mathematical Society in 2020, acknowledging their contributions to nonlinear partial differential equations, fluid dynamics, and free-boundary problems. Earlier in their career, they were a Fellow of the Alfred P. Sloan Foundation in 2000.

Best Publications

  • Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs

    Jerrold E. Marsden;George W. Patrick;Steve Shkoller

  • Well-posedness of the free-surface incompressible Euler equations with or without surface tension

    Daniel Coutand;Steve Shkoller

  • Motion of an Elastic Solid inside an Incompressible Viscous Fluid

    Daniel Coutand;Steve Shkoller

  • The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations

    Daniel Coutand;Steve Shkoller

  • Global well–posedness for the Lagrangian averaged Navier–Stokes (LANS–α) equations on bounded domains

    Jerrold E. Marsden;Steve Shkoller

  • Discrete Euler-Poincaré and Lie-Poisson equations

    Jerrold E. Marsden;Sergey Pekarsky;Steve Shkoller

  • Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum

    Daniel Coutand;Steve Shkoller

  • Variational Methods, Multisymplectic Geometry and Continuum Mechanics

    Jerrold E. Marsden;Sergey Pekarsky;Steve Shkoller;Matthew West

  • Multisymplectic geometry, covariant Hamiltonians, and water waves

    Jerrold E. Marsden;Steve Shkoller

  • Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence

    Kamran Mohseni;Branko Kosović;Steve Shkoller;Jerrold E. Marsden

  • Geometry and Curvature of Diffeomorphism Groups withH1Metric and Mean Hydrodynamics

    Steve Shkoller;Steve Shkoller

  • Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum

    Daniel Coutand;Steve Shkoller

  • The Anisotropic Lagrangian Averaged Euler and Navier-Stokes Equations

    Jerrold E. Marsden;Steve Shkoller

  • Nonuniqueness of weak solutions to the SQG equation

    Tristan Buckmaster;Steve Shkoller;Vlad Vicol

  • On the motion of an elastic solid inside of an incompressible viscous fluid

    Daniel Coutand;Steve Shkoller

  • On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations

    Daniel Coutand;Steve Shkoller

  • A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum

    Daniel Coutand;Hans Lindblad;Steve Shkoller

  • The geometry and analysis of the averaged Euler equations and a new diffeomorphism group

    Jerrold E. Marsden;Tudor S. Ratiu;Steve Shkoller

  • On the interaction between quasilinear elastodynamics and the Navier-Stokes equations

    Daniel Coutand;Steve Shkoller

  • Well-posedness of the Muskat problem with H2 initial data

    C.H. Arthur Cheng;Rafael Granero-Belinchón;Steve Shkoller

  • The Interaction between Quasilinear Elastodynamics and the

    Navier-Stokes Equations;Daniel Coutand;Steve Shkoller

  • Geometry and curvature of diffeomorphism groups with $H^1$ metric and mean hydrodynamics

    Steve Shkoller

Frequent Co-Authors

Jerrold E. Marsden
Jerrold E. Marsden California Institute of Technology
Vlad Vicol
Vlad Vicol Courant Institute of Mathematical Sciences
Tudor S. Ratiu
Tudor S. Ratiu École Polytechnique Fédérale de Lausanne
Darryl D. Holm
Darryl D. Holm Imperial College London
Hans Lindblad
Hans Lindblad Johns Hopkins University

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