Pathwise Solutions of the 2D Stochastic Primitive Equations

TL;DR

This paper proves the existence and uniqueness of strong solutions for a stochastic version of the 2D Primitive Equations, accommodating complex noise and realistic boundary conditions in oceanic and atmospheric models.

Contribution

It introduces novel analytical techniques to handle general nonlinear noise structures and physically relevant boundary conditions for stochastic Primitive Equations.

Findings

Established pathwise existence and uniqueness of solutions.

Developed new methods for nonlinear noise analysis.

Handled physically relevant boundary conditions.

Abstract

In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong solutions. The analysis employs novel techniques in contrast to previous works in order to handle a general class of nonlinear noise structures and to allow for physically relevant boundary conditions. The proof relies on Cauchy estimates, stopping time arguments and anisotropic estimates.