92-85 Collet P., Eckmann J.-P., Epstein H., Stubbe J.
A global attracting set for the Kuramoto-Sivashinsky equation (146K, Postscript) Jul 8, 92
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Abstract. New bounds are given for the $L^2$-norm of the solution of the Kuramoto-Shivashinsky equation $$\partial_t U(x,t) \,=\, -(\partial_x^2+\partial_x^4)U(x,t) - U(x,t)\partial_x U(x,t)~,$$ for initial data which are periodic with period $L$. There is no requirement on the antisymmetry of the initial data. The result is $$\limsup_{t\to\infty } \| U (\cdot, t) \|_2 \,\le\, \const L^{8/5}~.$$

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