Global existence on nonlinear Schrödinger-IMBq equations

Yonggeun Cho, Tohru Ozawa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)535-552
Number of pages18
JournalJournal of Mathematics of Kyoto University
Volume46
Issue number3
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Blow-up Criterion
Global Existence
Nonlinearity
BMO Space
Triebel-Lizorkin Space
Cauchy Problem
Energy

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Journal of Mathematics of Kyoto University, Vol. 46, No. 3, 2006, p. 535-552.

Research output: Contribution to journalArticle

@article{936bdfb83e854283878b0e4047ece720,
title = "Global existence on nonlinear Schr{\"o}dinger-IMBq equations",
abstract = "In this paper, we consider the Cauchy problem of Schr{\"O}dinger-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.",
author = "Yonggeun Cho and Tohru Ozawa",
year = "2006",
language = "English",
volume = "46",
pages = "535--552",
journal = "Kyoto Journal of Mathematics",
issn = "2156-2261",
publisher = "Kyoto University",
number = "3",

}

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 -