2 citations · 2 across the 8 of their papers we have counts for
10 papers
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…
Anomalous Dissipation at Onsager-Critical Regularity
Alexey Cheskidov, Qirui Peng
We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \c…
Global boundedness, absorbing sets and mass persistene in two-dimensional chemotaxis-Navier-Stokes systems with weakly singular sensitivity and sub-logistic sources
Minh Le, Alexey Cheskidov
This paper studies the following chemotaxis-fluid system in a two-dimensional bounded domain : \begin{equation*} \begin{cases} n_t + u \cdot \nabla n &= Δn - χ\nabla \cdot \left…
Instantaneous Type I blow-up and non-uniqueness of smooth solutions of the Navier-Stokes equations
Alexey Cheskidov, Mimi Dai, Stan Palasek
For any smooth, divergence-free initial data, we construct a solution of the Navier--Stokes equations that exhibits Type~I blow-up of the norm at time , while rem…