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papers

Publications (26)

2D homogeneous solutions to the Euler equation

Xue Luo, Roman Shvydkoy

A unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov's dissipation range

Alexey Cheskidov, Roman Shvydkoy

The essential spectrum of advective equations

Roman Shvydkoy

Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents

Roman Shvydkoy, Yuri Latushkin

Convex integration for a class of active scalar equations

Roman Shvydkoy

Global Well-Posedness Of A Non-Local Burgers Equation: The Periodic Case

Cyril Imbert, Roman Shvydkoy, Francois Vigneron

Nonlinear instability for the Navier-Stokes equations

Susan Friedlander, NataÅ¡a PavloviÄ, Roman Shvydkoy

The Energy Balance Relation for Weak solutions of the Density-Dependent Navier-Stokes Equations

Trevor Leslie, Roman Shvydkoy

Continuous spectrum of the 3D Euler equation is a solid annulus

Roman Shvydkoy

Homogeneous solutions to the 3D Euler system

Roman Shvydkoy

Global regularity for 2D Muskat equations with finite slope

Peter Constantin, Francisco Gancedo, Roman Shvydkoy +1

On the Rayleigh-Taylor instability in presence of a background shear

Roman Shvydkoy

Eulerian dynamics with a commutator forcing

Roman Shvydkoy, Eitan Tadmor

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

Roman Shvydkoy

Eulerian dynamics with a commutator forcing III. Fractional diffusion of order $0<Î±<1$

Roman Shvydkoy, Eitan Tadmor

The Energy Measure for the Euler and Navier-Stokes Equations

Trevor M. Leslie, Roman Shvydkoy

Conditions Implying Energy Equality for Weak Solutions of the Navier--Stokes Equations

Trevor M. Leslie, Roman Shvydkoy

Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces

Alexey Cheskidov, Roman Shvydkoy

A continuous model for turbulent energy cascade

Alexey Cheskidov, Susan Friedlander, Roman Shvydkoy

On the energy behavior of locally self-similar blowup for the Euler equation

Anne Bronzi, Roman Shvydkoy

The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity

Roman Shvydkoy, Susan Friedlander

Addendum: 2D homogeneous solutions to the Euler equation

Xue Luo, Roman Shvydkoy

On the energy of inviscid singular flows

Roman Shvydkoy

A study of energy concentration and drain in incompressible fluids

Roman Shvydkoy

On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$

Alexey Cheskidov, Roman Shvydkoy

Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation

Cyril Imbert, Tianling Jin, Roman Shvydkoy