Partial differential equations
A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 837-841.

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 H1(T), provided that the mass is less than 4π. Moreover, this mass threshold is independent of spatial periods.

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 H1(T), pourvu que la masse soit inférieure à 4π. En outre, ce seuil pour la masse est indépendant des périodes spatiales.

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DOI: 10.1016/j.crma.2015.06.015
Mosincat, Razvan 1, 2; Oh, Tadahiro 1, 2

1 School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
2 The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
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Mosincat, Razvan; Oh, Tadahiro. A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle. Comptes Rendus. Mathématique, Volume 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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