On the radius of analyticity of solutions to the cubic Szegő equation Academic Article uri icon

abstract

  • © 2013 Elsevier Masson SAS. 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).

author list (cited authors)

  • Gérard, P., Guo, Y., & Titi, E. S.

citation count

  • 10

publication date

  • January 2015