The large deviation principle for the stochastic 3D primitive equations with transport noise

TL;DR

This paper establishes a large deviation principle for 3D primitive equations with transport noise, addressing the impact of small-scale turbulence on large-scale geophysical fluid dynamics through advanced stochastic analysis.

Contribution

It proves the small-noise large deviation principle for 3D primitive equations with transport noise, including turbulent pressure effects, using novel energy bounds and handling both Stratonovich and Itô noise.

Findings

Large deviation principle established for stochastic primitive equations

Analysis includes turbulent pressure effects in transport noise

Results applicable to geophysical fluid dynamics modeling

Abstract

We prove the small-noise large deviation principle for the three-dimensional primitive equations with transport noise and turbulent pressure. Transport noise is important for geophysical fluid dynamics applications, as it takes into account the effect of small scales on the large scale dynamics. The main mathematical challenge is that we allow for the transport noise to act on the full horizontal velocity, therefore leading to a non-trivial turbulent pressure, which requires an involved analysis to obtain the necessary energy bounds. Both Stratonovich and It\^o noise are treated.