Translator Disclaimer
2018 On the global stability of a beta-plane equation
Fabio Pusateri, Klaus Widmayer
Anal. PDE 11(7): 1587-1624 (2018). DOI: 10.2140/apde.2018.11.1587

Abstract

We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common approximation in geophysical fluid dynamics and is referred to as the β -plane approximation. In vorticity formulation, the model we consider is then given by the Euler equation with the addition of a linear anisotropic, nondegenerate, dispersive term. This allows us to treat the problem as a quasilinear dispersive equation whose linear solutions exhibit decay in time at a critical rate.

Our main result is the global stability and decay to equilibrium of sufficiently small and localized solutions. Key aspects of the proof are the exploitation of a “double null form” that annihilates interactions between spatially coherent waves and a lemma for Fourier integral operators which allows us to control a strong weighted norm.

Citation

Download Citation

Fabio Pusateri. Klaus Widmayer. "On the global stability of a beta-plane equation." Anal. PDE 11 (7) 1587 - 1624, 2018. https://doi.org/10.2140/apde.2018.11.1587

Information

Received: 21 October 2016; Accepted: 4 March 2018; Published: 2018
First available in Project Euclid: 15 January 2019

zbMATH: 1393.35180
MathSciNet: MR3810467
Digital Object Identifier: 10.2140/apde.2018.11.1587

Subjects:
Primary: 35B34, 35Q35, 76B03, 76B15

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
38 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 7 • 2018
MSP
Back to Top