Work

Energy conservation and vanishing viscosity limit for the primitive equations

Year: 2026

Type: article

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.

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202526500272

Authors: Šárka Nečasová, Tong Tang, Emil Wiedemann, Lu Zhu

Institutions: Czech Academy of Sciences, Institute of Mathematics, Yangzhou University, Friedrich-Alexander-Universität Erlangen-Nürnberg, Hohai University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green