- 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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