## Journal of Mathematics of Kyoto University

### Global existence on nonlinear Schrödinger-IMBq equations

#### Abstract

In this paper, we consider the Cauchy problem of Schrödinger-IMBq equations in $\mathbb{R}^{n}$, $n \geq 1$. We first show the global existence and blowup criterion of solutions in the energy space for the 3 and 4 dimensional system without power nonlinearity under suitable smallness assumption. Secondly the global existence is established to the system with $p$-powered nonlinearity in $H^{s}(\mathbb{R}^{n})$, $n = 1,2$ for some $\frac{n}{2} < s < \mathrm{min}(2, p)$ and some $p > \frac{n}{2}$ . We also provide a blowup criterion for $n = 3$ in Triebel-Lizorkin space containing BMO space naturally.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 3 (2006), 535-552.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281748

Digital Object Identifier
doi:10.1215/kjm/1250281748

Mathematical Reviews number (MathSciNet)
MR2311358

Zentralblatt MATH identifier
1135.35071

#### Citation

Cho, Yonggeun; Ozawa, Tohru. Global existence on nonlinear Schrödinger-IMBq equations. J. Math. Kyoto Univ. 46 (2006), no. 3, 535--552. doi:10.1215/kjm/1250281748. https://projecteuclid.org/euclid.kjm/1250281748