Global solution and decay rate for a reduced gravity two and a half layer model

Abstract

In this paper we investigate the reduced gravity two and a half model in oceanic fluid dynamics. In a finite domain (for the initial-boundary value problem), we obtain time-independent estimates, which allow us to show the existence and uniqueness of regular solutions as well as the decay rate estimates. A collection of the decay rate estimates for $h_i-\widetilde{h}_i$ (with $\widetilde{h}_i$ being the stationary layer thickness) and $u_i(i = 1,2)$ in $L^2(Ω)$-norm as well as $H^1(Ω)$-norm as time $t \to \infty $ are established.