Estimates On The Lowest Dimension Of Inertial Manifolds For The Kuramoto-Sivasbinsky Equation In The General Case
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  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 Hm is bounded by a universal constant times L0.82m+2.05; 2. the lowest dimension of inertial manifolds in L2 is bounded by a universal constant times L1.64(ln L)0.2 where L = L/(2π√v).
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
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01 Jan 1994