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# Global existence on nonlinear Schrödinger-IMBq equations

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 Title: Global existence on nonlinear Schrödinger-IMBq equations Authors: Cho, Yonggeun Browse this author Ozawa, Tohru Browse this author Keywords: Cauchy problem Schr odinger-IMBq equations global existence blowup criterion Issue Date: 2005 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 744 Start Page: 1 End Page: 19 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69552 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics