What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (76.74%)
- Euler equations (31.01%)
- Sobolev space (20.93%)
What were the highlights of his more recent work (between 2015-2020)?
- Mathematical analysis (76.74%)
- Euler equations (31.01%)
- Mathematical physics (15.50%)
In recent papers he was focusing on the following fields of study:
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.
Between 2015 and 2020, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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