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

2025/10/31 by Manuel Fernando Cortez, Cortez, Manuel Fernando, Oscar Jarrín +1
Mathematics · Physics and Astronomy · Engineering · #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Fluid Dynamics and Thin Films

paper · pdf · doi:10.48550/arxiv.2510.27520

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.

Citations

• Sharp well-posedness and spatial decaying for a generalized dispersive-dissipative Kuramoto-type equation and applications to related models
• Spatial behavior of solutions for a large class of non-local PDE's\n arising from stratified flows
• On decay properties and asymptotic behavior of solutions to a non-local perturbed KdV equation
• On persistence properties in fractional weighted spaces
• New Asymptotic Profiles of Nonstationnary Solutions of the Navier-Stokes System

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