Global-in-time existence, uniqueness and stability of solutions to a model of the Antarctic Circumpolar Current

2024/09/25 by Luigi Roberti, Roberti, Luigi, Eduard Stefanescu +1
Engineering · Mathematics · Physics and Astronomy · #35B32 #35B35 #35Q31 #35R35 #76U60 #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2409.17013

openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a model for the Antarctic Circumpolar Current in rotating spherical coordinates. After establishing global-in-time existence and uniqueness of classical solutions, we turn our attention to the issue of stability of a class of steady zonal solutions (i.e., time-independent solutions that vary only with latitude). By identifying suitable conserved quantities and combining them to construct a Lyapunov function, we prove a stability result.

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