71 citations · 329 across the 39 of their papers we have counts for
10 papers · 1 filter
Ill-posedness of the Navier-Stokes and magneto-hydrodynamics systems
Alexey Cheskidov, Mimi Dai
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of weak solutions in a wide range of spaces. Speci…
Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
Alexey Cheskidov, Mimi Dai
Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a thr…
On the Onsager conjecture in two dimensions
A. Cheskidov, M. C. Lopes Filho, H. J. Nussenzveig Lopes +1
This note addresses the question of energy conservation for the 2D Euler system with an -control on vorticity. We provide a direct argument, based on a mollification in physic…
On the determining wavenumber for the nonautonomous subcritical SQG equation
Alexey Cheskidov, Mimi Dai
A time-dependent determining wavenumber was introduced in [5] to estimate the number of determining modes for the surface quasi-geostrophic (SQG) equation. In this paper we continu…
Regularity criteria for the 3D Navier-Stokes and MHD equations
Alexey Cheskidov, Mimi Dai
We prove that a solution to the 3D Navier-Stokes or MHD equations does not blow up at provided $\displaystyle \limsup_{q \to \infty} \int_{\mathcal{T}_q}^T \|Δ_q(\nabla \time…
Determining modes for the 3D Navier-Stokes equations
Alexey Cheskidov, Mimi Dai, Landon Kavlie
We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blo…