What question did this study set out to answer?

The research aims to identify sufficient conditions that prevent anomalous energy dissipation in Navier-Stokes equations.

March 15, 2026Open Access

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

Key Points

The research aims to identify sufficient conditions that prevent anomalous energy dissipation in Navier-Stokes equations.
Analyzed the three-dimensional incompressible Navier-Stokes equations within a bounded domain.
Explored conditions without assuming behavior of pressure near the boundary.
Utilized recent results on regularity for weak solutions of incompressible Euler equations.
Established a sufficient condition for the absence of anomalous energy dissipation.
Showed results without needing strong solutions for the Euler equations with the same initial data.

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.

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

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Abstract

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