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- Steve Shkoller

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
35
Citations
5,524
97
World Ranking
1904
National Ranking
814

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

- Mathematical analysis
- Quantum mechanics
- Geometry

His primary areas of study are Mathematical analysis, Euler equations, Geometry, Sobolev space and Navier–Stokes equations. His research in Mathematical analysis intersects with topics in Ricci curvature and Scalar curvature. The Euler equations study combines topics in areas such as Stokes operator, Boundary value problem, Singularity, Free surface and Degenerate energy levels.

He has researched Geometry in several fields, including Riemannian manifold and Submanifold. His Sobolev space study integrates concerns from other disciplines, such as Semi-implicit Euler method and Free boundary problem. His Navier–Stokes equations research is multidisciplinary, incorporating perspectives in Uniqueness theorem for Poisson's equation, Uniqueness, Reynolds stress equation model, Turbulence modeling and Existence theorem.

- Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs (521 citations)
- Well-posedness of the free-surface incompressible Euler equations with or without surface tension (369 citations)
- The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations (141 citations)

Steve Shkoller mostly deals with Mathematical analysis, Euler equations, Sobolev space, Compressibility and Euler's formula. His Mathematical analysis research includes themes of Stefan problem, Surface tension and Nonlinear system. The various areas that Steve Shkoller examines in his Euler equations study include Degenerate energy levels, Conservation law and Vorticity.

In his work, Curl, Bounded function and Pure mathematics is strongly intertwined with Vector field, which is a subfield of Sobolev space. His Compressibility research incorporates elements of Hyperbolic partial differential equation and Regularization. His Euler's formula research integrates issues from Flow, Reduction, Differential geometry and Mathematical physics.

- Mathematical analysis (76.74%)
- Euler equations (31.01%)
- Sobolev space (20.93%)

- Mathematical analysis (76.74%)
- Euler equations (31.01%)
- Mathematical physics (15.50%)

Steve Shkoller mainly focuses on Mathematical analysis, Euler equations, Mathematical physics, Vector field and Sobolev space. His Mathematical analysis research is multidisciplinary, relying on both Fluid dynamics, Stefan problem and Vorticity. Steve Shkoller focuses mostly in the field of Vorticity, narrowing it down to topics relating to Compressibility and, in certain cases, Free surface.

His work deals with themes such as Conservation law, Series and Nonlinear system, which intersect with Euler equations. His research in Vector field intersects with topics in Pure mathematics, Neumann boundary condition, Omega and Curl. He combines subjects such as Bounded function and Dirichlet distribution with his study of Sobolev space.

- Well-posedness of the Muskat problem with H2 initial data (77 citations)
- Nonuniqueness of weak solutions to the SQG equation (59 citations)
- On the Impossibility of Finite-Time Splash Singularities for Vortex Sheets (27 citations)

- Mathematical analysis
- Quantum mechanics
- Geometry

Steve Shkoller focuses on Mathematical analysis, Fluid dynamics, Open problem, Square root and Dissipative system. Steve Shkoller merges many fields, such as Mathematical analysis and Porous medium, in his writings. His Pointwise study incorporates themes from Step function, Compressibility, Curvature and Classification of discontinuities.

He interconnects Vorticity, Amplitude, Energy, Euler's formula and Conservative vector field in the investigation of issues within Euler equations. Steve Shkoller has included themes like Vortex sheet, Classical mechanics and Essential singularity in his Singularity theory study. His studies in Dirichlet distribution integrate themes in fields like Neumann boundary condition, Bounded function, Curl and Sobolev space.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs

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

Communications in Mathematical Physics **(1998)**

690 Citations

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

Daniel Coutand;Steve Shkoller.

Journal of the American Mathematical Society **(2007)**

394 Citations

Motion of an Elastic Solid inside an Incompressible Viscous Fluid

Daniel Coutand;Steve Shkoller.

Archive for Rational Mechanics and Analysis **(2005)**

229 Citations

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

Jerrold E. Marsden;Steve Shkoller.

Philosophical Transactions of the Royal Society A **(2001)**

197 Citations

The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations

Daniel Coutand;Steve Shkoller.

Archive for Rational Mechanics and Analysis **(2006)**

195 Citations

Discrete Euler-Poincaré and Lie-Poisson equations

Jerrold E. Marsden;Sergey Pekarsky;Steve Shkoller.

Nonlinearity **(1999)**

194 Citations

Variational Methods, Multisymplectic Geometry and Continuum Mechanics

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

Journal of Geometry and Physics **(2001)**

183 Citations

Multisymplectic geometry, covariant Hamiltonians, and water waves

Jerrold E. Marsden;Steve Shkoller.

Mathematical Proceedings of the Cambridge Philosophical Society **(1999)**

180 Citations

Geometry and Curvature of Diffeomorphism Groups withH1Metric and Mean Hydrodynamics

Steve Shkoller;Steve Shkoller.

Journal of Functional Analysis **(1998)**

167 Citations

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

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

Physics of Fluids **(2003)**

166 Citations

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