UC Irvine

This paper is concerned with the cubic Szego{double acute} equationi ∂t u = Π (| u |2 u), defined on the L2 Hardy space on the one-dimensional torus T, where Π : L2 (T) → L+2 (T) is the Szego{double acute} projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t ∈ (- ∞, ∞). In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the ℓ1 norm of Fourier transforms (the Wiener algebra). © 2013 Elsevier Masson SAS. All rights reserved.