Dynamic boundary conditions with noise for energy balance models coupled to geophysical flows

TL;DR

This paper studies an energy balance model coupled with geophysical flows under dynamic boundary conditions, demonstrating global well-posedness in both deterministic and stochastic settings for large data.

Contribution

It introduces a novel coupling with dynamic boundary conditions, including noise, and proves global well-posedness for large initial data in both deterministic and stochastic frameworks.

Findings

System is globally strongly well-posed in deterministic setting.

System is globally strongly well-posed in stochastic setting.

Applicable to large initial data in specified Sobolev spaces.

Abstract

This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the deterministic setting for arbitrary large data in $W^{2(1-\frac{1}{p}),p}$ for $p \in [2,\infty)$ and in the stochastic setting for arbitrary large data in $H^1$.