# 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);

 TeX DVI79Kb

## Abstract

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 20 Cauchy problem, Schr\"{o}dinger-IMBq equations, global existence, blowup criterion 35-xx PARTIAL DIFFERENTIAL EQUATIONS 1060