Global solutions of quasi-geostrophic shallow-water fronts

2022/03/03 by Yan, Fangchi, Zhang, Qingtian
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph)

paper · doi:10.48550/arxiv.2203.01967

Abstract

In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW front, which is a nonlinear, nonlocal dispersive equation, and prove the global existence of the solutions when the initial data is sufficiently close to a flat front.

Related

• Global solutions for a family of GSQG front equations
• Low regularity solutions for the surface quasi-geostrophic front equation
• Global solutions to the shallow-water system
• Global existence of strong solution for shallow water system with large initial data on the irrotational part
• Geodesic interpretation of the global quasi-geostrophic equations