The Cauchy problem for the nonlinear Schrödinger equation in H1
✍ Scribed by Thierry Cazenave; Fred B. Weissler
- Publisher
- Springer
- Year
- 1988
- Tongue
- English
- Weight
- 593 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0025-2611
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📜 SIMILAR VOLUMES
In this paper, we consider solutions of the L 2 -critical focusing nonlinear Schrödinger equation on R 2 for the initial data in H s (s < 1), mainly about the L 2 concentration phenomena for blow-up solutions and global well-posedness for small initial data.
We consider the Schrödinger equation in R 3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V , which is strictly larger than the standard H 1 -space due to the specific singularity exhibited by the solutions. We prove local existence