On the radius of analyticity of solutions to the cubic Szegő equation
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, p. 97-108
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This paper is concerned with the cubic Szegő equation $i{\partial }_{t}u=\Pi \left({|u|}^{2}u\right),$ defined on the ${L}^{2}$ Hardy space on the one-dimensional torus $𝕋$, where $\Pi :{L}^{2}\left(𝕋\right)\to {L}_{+}^{2}\left(𝕋\right)$ 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 $t\in \left(-\infty ,\infty \right)$. 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 ${\ell }^{1}$ norm of Fourier transforms (the Wiener algebra).

DOI : https://doi.org/10.1016/j.anihpc.2013.11.001
Classification:  35B10,  35B65,  47B35
Keywords: Cubic Szegő equation, Gevrey class regularity, Analytic solutions, Hankel operators
@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},
publisher = {Elsevier},
volume = {32},
number = {1},
year = {2015},
pages = {97-108},
doi = {10.1016/j.anihpc.2013.11.001},
zbl = {1332.35058},
mrnumber = {3303943},
language = {en},
url = {http://www.numdam.org/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, Volume 32 (2015) no. 1, pp. 97-108. doi : 10.1016/j.anihpc.2013.11.001. http://www.numdam.org/item/AIHPC_2015__32_1_97_0/

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