[Une remarque sur le caractère globalement bien posé de l'équation de Schrödinger non linéaire avec dérivée sur le cercle]
On considère dans cette note l'équation de Schrödinger avec dérivée sur le cercle. En particulier, en adaptant l'argument récent de Wu au cas periodique, on prouve que cette équation est globalement bien posée dans , pourvu que la masse soit inférieure à 4π. En outre, ce seuil pour la masse est indépendant des périodes spatiales.
In this note, we consider the derivative nonlinear Schrödinger equation on the circle. In particular, by adapting Wu's recent argument to the periodic setting, we prove its global well-posedness in , provided that the mass is less than 4π. Moreover, this mass threshold is independent of spatial periods.
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@article{CRMATH_2015__353_9_837_0,
author = {Mosincat, Razvan and Oh, Tadahiro},
title = {A remark on global well-posedness of the derivative nonlinear {Schr\"odinger} equation on the circle},
journal = {Comptes Rendus. Math\'ematique},
pages = {837--841},
publisher = {Elsevier},
volume = {353},
number = {9},
year = {2015},
doi = {10.1016/j.crma.2015.06.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.015/}
}
TY - JOUR AU - Mosincat, Razvan AU - Oh, Tadahiro TI - A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle JO - Comptes Rendus. Mathématique PY - 2015 SP - 837 EP - 841 VL - 353 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.06.015/ DO - 10.1016/j.crma.2015.06.015 LA - en ID - CRMATH_2015__353_9_837_0 ER -
%0 Journal Article %A Mosincat, Razvan %A Oh, Tadahiro %T A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle %J Comptes Rendus. Mathématique %D 2015 %P 837-841 %V 353 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.06.015/ %R 10.1016/j.crma.2015.06.015 %G en %F CRMATH_2015__353_9_837_0
Mosincat, Razvan; Oh, Tadahiro. A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 837-841. doi : 10.1016/j.crma.2015.06.015. http://www.numdam.org/articles/10.1016/j.crma.2015.06.015/
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