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Uncertainty estimates and<i>L</i><sub>2</sub>bounds for the Kuramoto–Sivashinsky equation
We consider the Kuramoto–Sivashinsky (KS) equation in one dimension with periodic boundary conditions. We apply a Lyapunov function argument similar to the one first introduced by Nicolaenko et al (1985 Physica D 16 155–83) and later improved by Collet et al (1993 Commun. Math. Phys. 152 203–14) and Goodman (1994 …