Sharp Ill-Posedness of the Euler Equations in Lorentz Spaces
arXiv:2605.16502Jeaheang Bang, Alexey Cheskidov
On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations
arXiv:2603.03666Alexey Cheskidov, Hedong Hou
Global boundedness and absorbing sets in two-dimensional chemotaxis-Navier-Stokes systems with weakly singular sensitivity and a sub-logistic source
arXiv:2512.24892Minh Le, Alexey Cheskidov
Anomalous Dissipation at Onsager-Critical Regularity
arXiv:2512.24568Alexey Cheskidov, Qirui Peng
Instantaneous Type I Blow-up and Non-uniqueness of Smooth Solutions of the Navier-Stokes Equations
arXiv:2511.09556Alexey Cheskidov, Mimi Dai, Stan Palasek
Global-in-time smooth solution to the Navier–Stokes equations for small initial data in frequency localized Koch–Tataru's space
arXiv:2503.11642Journal of Differential Equations, Volume 477, 2026, 114534.
Alexey Cheskidov, Taichi Eguchi
Global dissipative solutions of the 3D Naiver-Stokes and MHD equations
arXiv:2503.05692Alexey Cheskidov, Zirong Zeng, Deng Zhang
Existence and non-uniqueness of weak solutions with continuous energy to the 3D deterministic and stochastic Navier-Stokes equations
arXiv:2407.17463Advances in Mathematics, Volume 490, 2026, 110845.
Alexey Cheskidov, Zirong Zeng, Deng Zhang
An optimal upper bound on the determining wavenumber for 3D Navier-Stokes Equations
arXiv:2407.06474Nonlinear Differential Equations and Applications, Volume 33, 2026.
Alexey Cheskidov, Qirui Peng
Dissipation anomaly and anomalous dissipation in incompressible fluid flows
arxiv:2311.04182Alexey Cheskidov