71 citations · 329 across the 39 of their papers we have counts for
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Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces
Alexey Cheskidov, Roman Shvydkoy
We study the incompressible Navier-Stokes equations with a fractional Laplacian and prove the existence of discontinuous Leray-Hopf solutions in the largest critical space with arb…
Uniform global attractors for the nonautonomous 3D Navier-Stokes equations
Alexey Cheskidov, Songsong Lu
We obtain the existence and the structure of the weak uniform (with respect to the initial time) global attractor and construct a trajectory attractor for the 3D Navier-Stokes equa…
Norm Inflation for Generalized Navier-Stokes Equations
Alexey Cheskidov, Mimi Dai
We consider the incompressible Navier-Stokes equation with a fractional power of the Laplacian in the three dimensional case. We prove the existence of a smooth so…
Euler equations and turbulence: analytical approach to intermittency
A. Cheskidov, R. Shvydkoy
Physical models of intermittency in fully developed turbulence employ many phenomenological concepts such as active volume, region, eddy, energy accumulation set, etc, used to desc…