Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in H½

Razvan Mosincat

Research output: Contribution to journalArticlepeer-review

Abstract

We establish the global well-posedness of the derivative nonlinear Schrodinger
equation with periodic boundary condition in the Sobolev space H½ ,provided that the mass of initial data is less than 4. This result matches the one by Miao, Wu, and Xu and its recent mass threshold improvement by Guo and Wu in the non-periodic setting. Below H½, we show that the uniform continuity of the solution map on bounded subsets of Hs does not hold, for any gauge equivalent equation.
Original languageEnglish
Pages (from-to)4658 - 4722
Number of pages54
JournalJournal of Differential Equations
Volume263
Issue number8
Early online date8 Jun 2017
DOIs
Publication statusPublished - 15 Oct 2017

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