On the Radius of Analyticity of Solutions to the Cubic Szegő Equation

This paper is concerned with the cubic Szegő equation i∂tu = Π(|u|u), defined on the L Hardy space on the one-dimensional torus T, where Π : L(T)→ L+(T) is the Szegő 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 ` norm of Fourier transforms (the Wiener algebra).