Global existence on nonlinear Schr\"{o}dingerIMBq equations
Preprint Series # 744 Cho, Yonggeun and Ozawa, Tohru Global existence on nonlinear Schr\"{o}dingerIMBq equations. (2005); AbstractIn this paper, we consider the Cauchy problem of
Schr\"{o}dingerIMBq 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 TriebelLizorkin space containing BMO space
naturally. Item Type:  Preprint 

Additional Information:  20 

Uncontrolled Keywords:  Cauchy problem,
Schr\"{o}dingerIMBq equations, global existence, blowup criterion 

Subjects:  35xx PARTIAL DIFFERENTIAL EQUATIONS 

ID Code:  1060 

