Energy conservation and vanishing viscosity limit for the primitive equations

Nečasová Š, Tang T, Wiedemann E, Zhu L (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

DOI: 10.1142/S0218202526500272

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, Commun. Math. Phys. 370 (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.

Authors with CRIS profile

Emil Wiedemann Lehrstuhl für Analysis

Involved external institutions

Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ) Yangzhou University / 扬州大学 CN China (CN) Hohai University CN China (CN)

How to cite

APA:

Nečasová, Š., Tang, T., Wiedemann, E., & Zhu, L. (2026). Energy conservation and vanishing viscosity limit for the primitive equations. Mathematical Models & Methods in Applied Sciences. https://doi.org/10.1142/S0218202526500272

MLA:

Nečasová, Šárka, et al. "Energy conservation and vanishing viscosity limit for the primitive equations." Mathematical Models & Methods in Applied Sciences (2026).

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