Estimates On The Lowest Dimension Of Inertial Manifolds For The Kuramoto-Sivasbinsky Equation In The General Case

Author

Roger Temam
Xiaoming Wang, Missouri University of Science and TechnologyFollow

Abstract

We derive estimates on the lowest dimension in various Sobolev spaces of inertial manifolds for the Kuramoto-Sivashinsky equation:
(δu/δt) + vD⁴u+D²u+uDu=0
for solutions which are periodic with period L. Contrary to earlier results in [3] and other works, there is no requirement on the antisymmetry of the initial data. Our results are: 1. the lowest dimension of inertial manifolds in the Sobolev space H^m is bounded by a universal constant times L^0.82m+2.05; 2. the lowest dimension of inertial manifolds in L² is bounded by a universal constant times L^1.64(ln L)^0.2 where L = L/(2π√v).

Recommended Citation

R. Temam and X. Wang, "Estimates On The Lowest Dimension Of Inertial Manifolds For The Kuramoto-Sivasbinsky Equation In The General Case," Differential and Integral Equations, vol. 7, no. 3 thru 4, pp. 1095 - 1108, Project Euclid, Jan 1994.

The definitive version is available at https://doi.org/10.57262/die/1370267723

International Standard Serial Number (ISSN)

0893-4983

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Project Euclid, All rights reserved.

Publication Date

01 Jan 1994