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Cauchy problem for the -critical nonlinear Schrödinger equation below

✍ Scribed by Daoyuan Fang; Sijia Zhong

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
223 KB
Volume
62
Category
Article
ISSN
0362-546X

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Blowup in the Nonlinear Schrödinger Equa
Blowup in the Nonlinear Schrödinger Equation Near Critical Dimension
✍ Vivi Rottschäfer; Tasso J. Kaper 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 235 KB

This article contains an analysis of the cubic nonlinear Schrödinger equation and solutions that become singular in finite time. Numerical simulations show that in three dimensions the blowup is self-similar and symmetric. In two dimensions, the blowup still appears to be symmetric but is no longer