A global attracting set for the Kuramoto-Sivashinsky equation
type: Item
instance of: scholarly article
title: A global attracting set for the Kuramoto-Sivashinsky equation
zbMATH Open document ID: 0777.35073
DOI: 10.1007/BF02097064
author: P. Collet
author: Jean-Pierre Eckmann
author: Henri Epstein
author: Joachim Stubbe
published in: Communications in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: The authors give new bounds for the \(L^ 2\)-norm of the solution of the Kuramoto-Sivashinsky equation. This new bound is obtained by adapting a technique first initiated by \textit{R. Temam} [Infinite-dimensional dynamical systems in mechanics and physics (Springer, 1988; Zbl 0662.35001)]. This bound is equal to a constant multiplied by \(L^{8/5}\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 222068
zbMATH Keywords: bounds for the \(L^ 2\)-norm
zbMATH Keywords: Kuramoto-Sivashinsky equation
reviewed by: Guy Jumarie
MaRDI profile type: Publication
cites work: Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model
cites work: Q4862592
cites work: Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
cites work: Infinite-dimensional dynamical systems in mechanics and physics
full work available at URL: https://doi.org/10.1007/bf02097064
OpenAlex ID: W2013615321
Recommended article: Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation.
Recommended article: Q3610398
Recommended article: Q4232845
Recommended article: Global attractors of Kuramoto-Sivashinsky equations on the whole space \(\dot{L}^2(\varOmega)\)
Recommended article: The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D
Recommended article: Global attractor for axially symmetric Kuramoto-Sivashinsky equation in annular domains
Recommended article: Q4232935
Recommended article: Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
Recommended article: Q3729717
Recommended article: Q4504853
description: scientific article; zbMATH DE number 222068