Logo image
Back
On the Forced Surface Quasi-Geostrophic Equation: Existence of Steady States and Sharp Relaxation Rates
Journal article   Open access   Peer reviewed

On the Forced Surface Quasi-Geostrophic Equation: Existence of Steady States and Sharp Relaxation Rates

Fazel Hadadifard and Atanas G. Stefanov
Journal of mathematical fluid mechanics, v 23(1)
08 Feb 2021
DOI: https://doi.org/10.1007/s00021-021-00559-1
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
http://arxiv.org/abs/2008.09868View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Mathematics Mathematics, Applied Mechanics Physical Sciences Physics Physics, Fluids & Plasmas Science & Technology Technology
We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori estimates for them. Importantly, to do so, we only impose minimal cancellation conditions on the forcing function. Our main result is that all L-1 boolean AND L-infinity localized initial data produces global solutions of the forced SQG, which converge to the steady states in L-p(R-2), 1 < p <= 2 as time goes to infinity. This establishes that the steady states serve as one point attracting set. Moreover, by employing the method of scaling variables, we compute the sharp relaxation rates, by requiring slightly more localized initial data.

Metrics

8 Record Views
2 citations in Web of Science
2 citations in Scopus

Details

UN Sustainable Development Goals (SDGs)

This publication has contributed to the advancement of the following goals:

#13 Climate Action

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics, Applied
Mechanics
Physics, Fluids & Plasmas
Logo image