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.
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 language | English |
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Pages (from-to) | 4658 - 4722 |
Number of pages | 54 |
Journal | Journal of Differential Equations |
Volume | 263 |
Issue number | 8 |
Early online date | 8 Jun 2017 |
DOIs | |
Publication status | Published - 15 Oct 2017 |