71 citations · 329 across the 39 of their papers we have counts for
43 papers
Global dissipative solutions of the 3D Naiver-Stokes and MHD equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
For any divergence free initial data in , we prove the existence of infinitely many dissipative solutions to both the 3D Navier-Stokes and MHD equations, whose energy pr…
Existence and non-uniqueness of weak solutions with continuous energy to the 3D deterministic and stochastic Navier-Stokes equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data ther…
Dyadic models for fluid equations: a survey
Alexey Cheskidov, Mimi Dai, Susan Friedlander
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beau…
Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions
Alexey Cheskidov, Xiaoyutao Luo
In this paper, we revisit the notion of temporal intermittency to obtain sharp nonuniqueness results for linear transport equations. We construct divergence-free vector fields with…
Volumetric theory of intermittency in fully developed turbulence
Alexey Cheskidov, Roman Shvydkoy
This study introduces a new family of volumetric flatness factors which give a rigorous parametric description of the phenomenon of intermittency in fully developed turbulent flows…
The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence
Alexey Cheskidov, Mimi Dai
We estimate the number of degrees of freedom of solutions of the 2D Navier-Stokes equation, proving that its mathematical analog, the number of determining modes, is bounded by the…