Global existence on nonlinear Schr\"{o}dinger-IMBq equations
Global existence on nonlinear Schr\"{o}dinger-IMBq equations
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DOI：
10.1215/kjm/1250281748
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发表时间：
2005
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影响因子：
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通讯作者：
Yonggeun Cho;T. Ozawa
中科院分区：
文献类型：
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作者：
Yonggeun Cho;T. Ozawa
本文考虑$\mathbb{R}^n, n \ge 1$中Schrödinger-IMBq方程的柯西问题。在适当的小度假设下，首先给出了无幂非线性的3维和4维系统在能量空间解的整体存在性和爆破判据。其次，建立了在$H^s(\mathbb{R}^n), n = 1, 2$上对某些$\frac n2 < s \frac n2$具有$p$动力非线性的系统的整体存在性。并给出了自然包含BMO空间的Triebel-Lizorkin空间中$n = 3$的爆破判据。
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 $\frac n2 < s \frac n2$. We also provide a blowup criterion for $n = 3$ in Triebel-Lizorkin space containing BMO space naturally.