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On the absence of anomalous dissipation for the Navier-Stokes equations with Navier boundary conditions: a sufficient condition

Year: 2025

Type: preprint

Abstract: We consider the three-dimensional incompressible Navier-Stokes equations in a bounded domain with Navier boundary conditions. We provide a sufficient condition for the absence of anomalous energy dissipation without making assumptions on the behaviour of the corresponding pressure near the boundary or the existence of a strong solution to the incompressible Euler equations with the same initial data. We establish our result by using our recent regularity results for the pressure corresponding to weak solutions of the incompressible Euler equations [Arch. Ration. Mech. Anal., 249 (2025), 28].

Source: arXiv (Cornell University)

DOI: 10.17863/cam.128140

Authors: Bardos, Claude, Boutros, Daniel, Titi, Edriss S

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Texas AgriLife Research, Weizmann Institute of Science, Universität Wien, Centre National de la Recherche Scientifique

OpenAlex ID: W7135220451

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