Time-periodic solutions to an energy balance model coupled with an active fluid under arbitrary large forces

TL;DR

This paper proves the existence of at least one strong time-periodic solution to a coupled energy balance and fluid model, even with arbitrarily large periodic forcing, advancing understanding of climate and fluid dynamics models.

Contribution

It establishes the existence of time-periodic solutions for a coupled climate-fluid model without requiring small forcing conditions, allowing for large external influences.

Findings

Existence of at least one strong time-periodic solution.

Solutions exist under arbitrarily large periodic forcing.

The model couples energy balance with primitive fluid equations.

Abstract

This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at least one strong time-periodic solution, provided the forcing term is time-periodic. The forcing term does not need to satisfy a smallness condition and is allowed to be arbitrarily large.