Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4604234 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2015 | 12 Pages |
Abstract
This paper is concerned with the cubic Szegő equationi∂tu=Π(|u|2u),i∂tu=Π(|u|2u), defined on the L2L2 Hardy space on the one-dimensional torus TT, where Π:L2(T)→L+2(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∈(−∞,∞)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 ℓ1ℓ1 norm of Fourier transforms (the Wiener algebra).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Patrick Gérard, Yanqiu Guo, Edriss S. Titi,