What question did this study set out to answer?

The central aim is to establish a strengthened large deviation principle (LDP) for stochastic primitive equations modeling anisotropic geophysical flows.

March 15, 2026

Strengthened Large Deviation Principle via Pathwise Regularity for Anisotropic Stochastic Primitive Equations

Puntos clave

The central aim is to establish a strengthened large deviation principle (LDP) for stochastic primitive equations modeling anisotropic geophysical flows.
Utilized the weak convergence method to establish an LDP in a specified space.
Analyzed the solutions' pathwise regularity under small noise conditions.
Addressed the challenges of intrinsic anisotropy, particularly in the convection term.
Demonstrated that solutions possess enhanced pathwise regularity, belonging almost surely to a particular space.
Strengthened the LDP to a finer topology, providing a more precise asymptotic behavior description.
Showed notable differences from traditional anisotropic Navier-Stokes cases.

Resumen

This paper establishes the large deviation principle (LDP) for the two-dimensional stochastic primitive equations with horizontal viscosity, a model for anisotropic geophysical flows under small noise. Using the weak convergence method, we first prove an LDP in the space Formula: see text. The main novelty lies in demonstrating that the solutions possess enhanced pathwise regularity, belonging almost surely to Formula: see text. This stronger regularity allows us to subsequently strengthen the LDP to the finer topology of Formula: see text, providing a more precise description of the asymptotic behavior. The analysis requires handling the intrinsic anisotropy of the system, particularly in the convection term, which introduces technical challenges distinct from the anisotropic Navier-Stokes cases.

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