On the radius of analyticity of solutions to the cubic Szego equation
Article
Gérard, P, Guo, Y, Titi, ES. (2015). On the radius of analyticity of solutions to the cubic Szego equation
. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 32(1), 97-108. 10.1016/j.anihpc.2013.11.001
Gérard, P, Guo, Y, Titi, ES. (2015). On the radius of analyticity of solutions to the cubic Szego equation
. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 32(1), 97-108. 10.1016/j.anihpc.2013.11.001
This paper is concerned with the cubic Szego equationi {equation presented}, defined on the L2 Hardy space on the one-dimensional torus T, where π : L2(T)→L2+(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 ∈(-infin;,∞). 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).
