Journal of Mathematics of Kyoto University

Global existence on nonlinear Schrödinger-IMBq equations

Yonggeun Cho and Tohru Ozawa

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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

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

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]


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.

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