Author

Alexey Cheskidov

3 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Oct 2026

Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy

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 positive times. When the initial data belong to the Sobolev spaces $W^{-1,p}$ for $1<p<\infty$, our constructed solutions are weak in the clas...

Alexey Cheskidov, He-Dong Hou · 0 citations

Sep 2026

Global dissipative solutions of the 3D Navier–Stokes and MHD equations

For any nontrivial divergence‐free initial data in H12$H^\frac{1}{2}$ , we prove the existence of infinitely many dissipative solutions to both the 3D Navier–Stokes and MHD equations, whose energy profiles are continuous and decreasing on [0,∞)$[0,\infty)$ . If the initial data is only L2$L^2$ , our construction yields...

Alexey Cheskidov, Zi-Rong Zeng, Deng Zhang · Proceedings of the London Ma... · 0 citations

Preprint Oct 2026

Inverse Energy Cascade and Non-uniqueness for the Advection-Diffusion Equation

We prove non-uniqueness for the advection-diffusion equation with a drift in a logarithmically near-critical class below $L_t^2L_x^\infty$. The first construction is a diffusion-assisted inverse cascade of scalar energy that diverges as $t \to 0$. The second uses compressed inverse mixing, with diffusion acting perturb...

Alexey Cheskidov, Xiao-Ran Liu · 0 citations