PreprintCC BY 4.0arXiv
On energy equality of the 3D anisotropic Navier-Stokes equations
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.
Related
- Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality
- Energy equality and renormalization of Navier-Stokes-Vlasov equations
- On the stability of solutions to the 3-D anisotropic Navier-Stokes equations in the critical space
- An Anisotropic Onsager Criterion for the Two-Dimensional Navier--Stokes Equations with Horizontal Viscosity
- Global Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation
BibTeX
@misc{ye2026energy,
title = {{On energy equality of the 3D anisotropic Navier-Stokes equations}},
author = {Yulin Ye and Wei Wei and Yanqing Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12383},
eprint = {2609.12383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12383},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On energy equality of the 3D anisotropic Navier-Stokes equations
AU - Yulin Ye
AU - Wei Wei
AU - Yanqing Wang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12383
UR - https://arxiv.org/abs/2609.12383
AB - 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.
ER -