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

Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S.

Gérard, Patrick ; Guo, Yanqiu ; Titi, Edriss S.

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 97-108 / Harvested from Numdam

Résumé

This paper is concerned with the cubic Szegő equation $i \partial_{t} u = Π ({| u |}^{2} u),$ defined on the $L^{2}$ Hardy space on the one-dimensional torus $𝕋$ , where $Π : L^{2} (𝕋) \to L_{+}^{2} (𝕋)$ 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 $t \in (- \infty, \infty)$ . 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).

Publié le : 2015-01-01

MR 3303943 | Zbl 1332.35058

DOI : https://doi.org/10.1016/j.anihpc.2013.11.001
Classification: 35B10, 35B65, 47B35

@article{AIHPC_2015__32_1_97_0,
     author = {G\'erard, Patrick and Guo, Yanqiu and Titi, Edriss S.},
     title = {On the radius of analyticity of solutions to the cubic Szeg\H o equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {32},
     year = {2015},
     pages = {97-108},
     doi = {10.1016/j.anihpc.2013.11.001},
     mrnumber = {3303943},
     zbl = {1332.35058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2015__32_1_97_0}
}

Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S. On the radius of analyticity of solutions to the cubic Szegő equation. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) pp. 97-108. doi : 10.1016/j.anihpc.2013.11.001. http://gdmltest.u-ga.fr/item/AIHPC_2015__32_1_97_0/

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