Abstract
We recall that in the case of the Kuramoto—Sivashinsky [HN, HN1,HNZ, NSh] equation on the space H of odd L-periodic functions, (du/dt)+Au+R(u)=0, we have
with
with the explicit time-independent ϕ defined in [FNST, FNST1],
(Here as in the sequel c0, c1 … denote absolute constants; for instance, c0 = (2π)4.) Also we shall consider L ≥ 1, the case L < 1 being of no interest.
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© 1989 Springer-Verlag New York Inc.
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Constantin, P., Foias, C., Nicolaenko, B., Teman, R. (1989). Application: The Kuramoto—Sivashinsky Equation. In: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematical Sciences, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3506-4_16
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DOI: https://doi.org/10.1007/978-1-4612-3506-4_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8131-3
Online ISBN: 978-1-4612-3506-4
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