Energy decay of solutions to the Boussinesq, primitive, and planetary geostrophic equations
type: Item
instance of: scholarly article
title: Energy decay of solutions to the Boussinesq, primitive, and planetary geostrophic equations
zbMATH Open document ID: 0938.35145
author: G. K. Vallis
author: Maria E. Schonbek
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-11-02T00:00:00Z
review text: The authors study in the whole \(\mathbb{R}^3\) the long-time behaviour of the energy of solutions to the basic equations modelling atmospheric and oceanic flows. More precisely, under consideration are Boussinesq, primitive, and planetary geostrophic equations. Using the Fourier splitting method, it is shown that the asymptotic long-time behaviour depends on the type of data, and on the number of non-zero damping constants in the equations. In several particular cases, the authors establish an algebraic rate of decay or ocsillating behaviour for \(t\to\infty\).
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 1334720
zbMATH Keywords: Boussinesq equations
zbMATH Keywords: primitive equations
zbMATH Keywords: long-time behaviour of energy
zbMATH Keywords: planetary geostrophic equations
zbMATH Keywords: Fourier splitting method
zbMATH Keywords: non-zero damping constants
zbMATH Keywords: algebraic rate of decay
zbMATH Keywords: ocsillating behaviour
Wikidata QID: Q57918162
MaRDI profile type: Publication
OpenAlex ID: W2007906347
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cites work: Q3766216
cites work: Q4162803
cites work: Decay Results for Weak Solutions of the Navier-Stokes Equations on Rn
DOI: 10.1006/JMAA.1999.6354
description: scientific article; zbMATH DE number 1334720