Energy Conservation and Vanishing Viscosity Limit for the Primitive Equations
Abstract
In this paper, we consider the problem of energy conservation for weak solutions of the inviscid Primitive Equations (PE) in a bounded domain. Based on the work [Bardos et al., Onsager's conjecture with physical boundaries and an application to the vanishing viscosity limit, Comm. Math. Phys., 2019, 291-310], we prove the energy conservation for PE with boundary condition under suitable Onsager-type assumptions. But due to the special structure of PE system and its domain, some new challenging difficulties arise: the lack of information about the vertical velocity, and existing corner points in the domain. We introduce some new ideas to overcome the above obstacles. As a byproduct, we give a sufficient condition for absence of anomalous energy dissipation in the vanishing viscosity limit.
Keywords
Cite
@article{arxiv.2505.15658,
title = {Energy Conservation and Vanishing Viscosity Limit for the Primitive Equations},
author = {Šárka Nečasová and Tong Tang and Emil Wiedemann and Lu Zhu},
journal= {arXiv preprint arXiv:2505.15658},
year = {2025}
}
Comments
19 pages, 2 figures