Persistence property and analyticity for a shallow-water model with the coriolis effect in weighted spaces

Abstract

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.