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June  2019, 24(6): 2613-2638. doi: 10.3934/dcdsb.2018267

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

 1 School of Mathematics, Northwest University, Xi'an 710127, China 2 School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China

* Corresponding author: Lei Yao

Received  December 2017 Revised  April 2018 Published  October 2018

Fund Project: Liu and Yao were supported by the National Natural Science Foundation of China #11571280, 11331005, FANEDD #201315

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.

Citation: Yongming Liu, Lei Yao. Global solution and decay rate for a reduced gravity two and a half layer model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2613-2638. doi: 10.3934/dcdsb.2018267
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