September 16, 2025Open Access

Stability of the 3D Navier–Stokes equations with anisotropic dissipation

Key Points

Global existence is demonstrated for the Navier–Stokes equations under anisotropic dissipation conditions.
The stability of the equations indicates potential applications in modeling complex fluid behaviors.
Results have implications for various physical contexts, including anisotropic turbulence and strongly stratified fluids.
This work enhances the understanding of stability in fluid dynamics under specific dissipation influences.

Abstract

Abstract This paper establishes the global existence and stability of the Navier–Stokes equations with dissipation acting in the vertical direction and on the vertical average in one of the horizontal directions. This Navier–Stokes model arises in various physical contexts such as strongly stratified fluids and anisotropic turbulence models.

Stability of the 3D Navier–Stokes equations with anisotropic dissipation

Key Points

Abstract

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