Remarks on the Spatial Asymptotic Behavior of Solutions to a 1D Model of Equatorial Oceanic Flows

Abstract

We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Molinet, Global Existence and Finite-Time Blow-Up for a Nonlinear Nonlocal Evolution Equation, Commun. Math. Phys. 402 (2023), 3233-3252]. We investigate the spatial asymptotic behavior of its solutions. In particular, we observe the influence of the Coriolis effect, which, even for rapidly decaying initial data, yields solutions that decay at the rate $1 / |x|$. Thereafter, we shed light on the optimality of this decay rate.