Existence and generalized Gevrey regularity of solutions to the Kuramoto–Sivashinsky equation in R

Motivated by the work of Foias and Temam [C. Foias, R. Temam, Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Funct. Anal. 87 (1989) 359–369], we prove the existence and Gevrey regularity of local solutions to the Kuramoto–Sivashinsky equation in Rn with initial data in the space of distributions. The control on the Gevrey norm provides an explicit estimate of the analyticity radius in terms of the initial data. In the particular case when n = 1, our analysis allows for initial data that are less smooth than that considered by Grujić and Kukavica [Z. Grujić, I. Kukavica, Space analyticity for the Navier–Stokes and related equations with initial data in Lp , J. Funct. Anal. 152 (1998) 447–466]. © 2007 Elsevier Inc. All rights reserved. MSC: primary 35Q20; secondary 35Q35