Collet P., Eckmann J.-P., Epstein H., Stubbe J.
Analyticity for the Kuramoto-Sivashinsky Equation
(164K, Postscript)
ABSTRACT. We study the analyticity properties of solutions of the
Kuramoto-Sivashinsky 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 $L$.
Numerical experiments are presented which show that the solutions of the
\KS-equation are analytic in a strip around the real axis whose width
is independent
of
$L$. A rigorous lower bound $O(L^{-16/25})$ is given for this width.