Stationary and discontinuous weak solutions of the Navier-Stokes equations
Analysis of PDEs
2020-08-24 v5
Abstract
We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme utilizing new stationary building blocks designed specifically for the NSE. The constructed family of approximate stationary solutions is also used to prove the existence of weak solutions of the NSE with energy profiles discontinuous on a dense set of positive Lebesgue measure.
Keywords
Cite
@article{arxiv.1901.07485,
title = {Stationary and discontinuous weak solutions of the Navier-Stokes equations},
author = {Alexey Cheskidov and Xiaoyutao Luo},
journal= {arXiv preprint arXiv:1901.07485},
year = {2020}
}
Comments
Unfortunately, a critical error was found in the construction in Section 3 and the weak solutions constructed based on the building blocks in Section 3 were not divergence-free