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

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 $p\in [2,\mathrm{\infty })$ and in the stochastic setting for arbitrary large data in $H^1$.