### Abstract

In this paper, we consider the Cauchy problem of SchrÖdinger-IMBq equations in ℝ^{n}, n ≥ 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} (ℝ^{n}), n = 1, 2 for some n/2 < s < min(2, p) and some p > n/2. We also provide a blowup criterion for n = 3 in Triebel-Lizorkin space containing BMO space naturally.

Original language | English |
---|---|

Pages (from-to) | 535-552 |

Number of pages | 18 |

Journal | Journal of Mathematics of Kyoto University |

Volume | 46 |

Issue number | 3 |

Publication status | Published - 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Mathematics of Kyoto University*,

*46*(3), 535-552.

**Global existence on nonlinear Schrödinger-IMBq equations.** / Cho, Yonggeun; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Journal of Mathematics of Kyoto University*, vol. 46, no. 3, pp. 535-552.

}

TY - JOUR

T1 - Global existence on nonlinear Schrödinger-IMBq equations

AU - Cho, Yonggeun

AU - Ozawa, Tohru

PY - 2006

Y1 - 2006

N2 - In this paper, we consider the Cauchy problem of SchrÖdinger-IMBq equations in ℝn, n ≥ 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 Hs (ℝn), n = 1, 2 for some n/2 < s < min(2, p) and some p > n/2. We also provide a blowup criterion for n = 3 in Triebel-Lizorkin space containing BMO space naturally.

AB - In this paper, we consider the Cauchy problem of SchrÖdinger-IMBq equations in ℝn, n ≥ 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 Hs (ℝn), n = 1, 2 for some n/2 < s < min(2, p) and some p > n/2. We also provide a blowup criterion for n = 3 in Triebel-Lizorkin space containing BMO space naturally.

UR - http://www.scopus.com/inward/record.url?scp=33947576598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947576598&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33947576598

VL - 46

SP - 535

EP - 552

JO - Kyoto Journal of Mathematics

JF - Kyoto Journal of Mathematics

SN - 2156-2261

IS - 3

ER -