In this paper, we consider an asymptotic model for wave propagation in shallow water with the effect of the Coriolis force is derived from the governing equation in two dimensional flows. Motivated by the eariler works (Brandolese in Int Math Res Not 22:5161–5181, 2012; Escauriaza et al. in J Funct Anal 244:504–535, 2007; Himonas et al. in Commun Math Phys 271:511–522, 2007; Himonas and Misiolek in Math Ann 327:575–584, 2003; Kohlmann in Z Angew Math Mech 94:264–272, 2014), we demonstrate the persistence results for the solution in weighted \(L^p\) spaces for a large classs of moderate weights. We also discuss the spatial asymptotic profiles of solutions to this model equation. Finally, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.

在本文中，我们考虑了二维流动中的控制方程，推导了在科里奥利力作用下浅水波传播的渐近模型。受到早期工作人员的激励（Brandolese in Int Math Res Not 22：5161-5181，2012; Escauriaza等人在J Funct Anal 244：504-535，2007; Himonas等人在Commun Math Phys 271：511–522， 2007; Himonas和Misiolek在Math Ann 327：575–584，2003; Kohlmann在Z Angew Math Mech 94：264–272，2014）中，我们证明了加权\（L ^ p \）空间中解的持久性结果中等重量的一大类。我们还将讨论该模型方程解的空间渐近曲线。最后，通过分析初始数据，我们表明其解决方案可以同时分析全局和时间局部变量。