This analysis demonstrates global existence and stability of Navier–Stokes equations with anisotropic dissipation, suggesting important applications in stratified fluids.
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.
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Cao et al. (2025) studied this question.
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