2 citations · 2 across the 8 of their papers we have counts for
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Admissible solutions of the Euler equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
In this paper, we prove the existence of an extensive class of initial data--characterized by intermittency dimension and roughness--for which the d-dimensional Euler equations (d…
Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
Alexey Cheskidov, Hedong Hou
We prove the global existence of solutions to the Navier-Stokes equations for any divergence-free distributional initial data. The solutions are smooth in both time and space at po…
Cascade mechanisms for Navier-Stokes blow-up
Alexey Cheskidov, Mimi Dai, Stan Palasek
In a recent preprint (arXiv:2511.09556), we exhibited an inverse energy cascade for the 3D Navier-Stokes equations which results in "instantaneous" Type I blow-up and failure of un…
Sharp Ill-Posedness of the Euler Equations in Lorentz Spaces
Jeaheang Bang, Alexey Cheskidov
We study vortex stretching for the three-dimensional axisymmetric Euler equations without swirl in vorticity formulation. Danchin (2007) established global existence and uniqueness…
On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations
Alexey Cheskidov, Hedong Hou
We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivia…