Abstract
We prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schrodinger equation. Precisely we show that a unique and global solution exists for initial data in the Sobolev space Hs(ℝ) for any [image omitted]. This improves the result in [25], where global well-posedness was established for any [image omitted]. We use the I-method to take advantage of the conservation laws of the equation. The new ingredient in our proof is an interaction Morawetz estimate for the smoothed out solution Iu. As a byproduct of our proof we also obtain that the Hs norm of the solution obeys polynomial-in-time bounds.
Original language | English (US) |
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Pages (from-to) | 1395-1429 |
Number of pages | 35 |
Journal | Communications in Partial Differential Equations |
Volume | 33 |
Issue number | 8 |
DOIs | |
State | Published - Aug 26 2008 |
Externally published | Yes |
Keywords
- Global well-posedness
- Morawetz estimates
- Schrodinger equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics