×

Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. (English) Zbl 1152.35491

Summary: We prove an “almost conservation law” to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in \(H^s(\mathbb{R}^n)\) when \(n = 2, 3\) and \(s > 4/7, 5/6\), respectively.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35L65 Hyperbolic conservation laws
PDF BibTeX XML Cite
Full Text: DOI arXiv