Year: 2026
Type: preprint
Abstract: In the spirit of the recent work by Demmel and Wiedemann \cite{[DW]}, we investigate the validity of the energy balance law for weak solutions to the three-dimensional Navier-Stokes equations with only horizontal dissipation. We prove that famous Lions-Shinbrot type energy conservation criteria, originally established for the classical isotropic Navier-Stokes equations, continue to hold in this anisotropic setting. Furthermore, we present two distinct approaches that handle the torus case and the whole space case, respectively.
Source: arXiv (Cornell University)
Authors: Ye, Yulin, Wei, Wei, Wang, Yanqing
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213113353