On the radius of analyticity of solutions to the cubic Szego equation

This paper is concerned with the cubic Szego equation i partial derivative(t)u = Pi(vertical bar u vertical bar(2)u), defined on the L-2 Hardy space on the one-dimensional torus T, where Pi : L-2 (T) -> L-+(2)(T) is the Szego projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t is an element of (-infinity, infinity). 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 l(1) norm of Fourier transforms (the Wiener algebra). (C) 2013 Elsevier Masson SAS. All rights reserved.