 9285 Collet P., Eckmann J.P., Epstein H., Stubbe J.
 A global attracting set for the KuramotoSivashinsky equation
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Jul 8, 92

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Abstract. New bounds are given for the $L^2$norm of the solution of the
KuramotoShivashinsky 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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