Collet, Pierre; Eckmann, Jean-Pierre; Epstein, Henri; Stubbe, Joachim A global attracting set for the Kuramoto-Sivashinsky equation. (English) Zbl 0777.35073 Commun. Math. Phys. 152, No. 1, 203-214 (1993). 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 R. Temam [Infinite-dimensional dynamical systems in mechanics and physics (Springer, 1988; Zbl 0662.35001)]. This bound is equal to a constant multiplied by \(L^{8/5}\). Reviewer: G.Jumarie (Montreal) Cited in 1 ReviewCited in 71 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37C75 Stability theory for smooth dynamical systems Keywords:bounds for the \(L^ 2\)-norm; Kuramoto-Sivashinsky equation Citations:Zbl 0662.35001 PDFBibTeX XMLCite \textit{P. Collet} et al., Commun. Math. Phys. 152, No. 1, 203--214 (1993; Zbl 0777.35073) Full Text: DOI References: [1] [Felen] Frisch, U., She, Z. S., Thual, O.: Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model. J. Fluid Mech.168, 221–240 (1986) · Zbl 0597.76006 [2] [Il] Ilyashenko, Yu.S.: Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation. J. Dyn. Differ. Equations, in print [3] [M] Manneville, P.: Dissipative Structures and Weak Turbulence, San Francisco-London, Academic Press, 1989 · Zbl 0839.76035 [4] [Nelen] Nicolaenko, B., Scheurer, B., Temam, R.: Some global dynamical properties of the Kuramoto-Sivashinsky equations: Nonlinear, stability and attractors. PhysicaD16, 155–183 (1985) · Zbl 0592.35013 [5] [T] Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics. Berlin, Heidelberg, New York: Springer, 1988 · Zbl 0662.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.