44 citations · 110 across the 10 of their papers we have counts for
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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
Motivated by Kolmogorov's theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wav…
Ill-posedness of basic equations of fluid dynamics in Besov spaces
A. Cheskidov, R. Shvydkoy
We give a construction of a divergence-free vector field , for all , such that any Leray-Hopf solution to the Navier-Stokes equation…
The vanishing viscosity limit for a dyadic model
Alexey Cheskidov, Susan Friedlander
A dyadic shell model for the Navier-Stokes equations is studied in the context of turbulence. The model is an infinite nonlinearly coupled system of ODEs. It is proved that the uni…
On the regularity of weak solutions of the 3D Navier-Stokes equations in
Alexey Cheskidov, Roman Shvydkoy
We show that if a Leray-Hopf solution to the 3D Navier-Stokes equation belongs to or its jumps in the -norm do not ex…
On the energy equality for weak solutions of the 3D Navier-Stokes equations
A. Cheskidov, S. Friedlander, R. Shvydkoy
We prove that the energy equality holds for weak solutions of the 3D Navier-Stokes equations in the functional class , where is the domain of the frac…
An inviscid dyadic model of turbulence: the global attractor
Alexey Cheskidov, Susan Friedlander, Natasa Pavlović
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an…