Dept. Math, Hokkaido Univ. EPrints Server

Global existence on nonlinear Schr\"{o}dinger-IMBq equations

Preprint Series # 744
Cho, Yonggeun and Ozawa, Tohru Global existence on nonlinear Schr\"{o}dinger-IMBq equations. (2005);

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In this paper, we consider the Cauchy problem of Schr\"{o}dinger-IMBq equations in $\mathbb{R}^n, n \ge 1$. 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 $\frac n2 < s < \min(2,p)$ and some $p > \frac n2$. We also provide a blowup criterion for $n = 3$ in Triebel-Lizorkin space containing BMO space naturally.

Item Type:Preprint
Additional Information:20
Uncontrolled Keywords:Cauchy problem, Schr\"{o}dinger-IMBq equations, global existence, blowup criterion
ID Code:1060