Minimal-mass blowup solutions of the mass-critical NLS
文献类型：期刊论文
| 作者 | Tao, Terence1; Visan, Monica; Zhang, Xiaoyi2 |
| 刊名 | FORUM MATHEMATICUM
 |
| 出版日期 | 2008 |
| 卷号 | 20期号:5页码:881-919 |
| ISSN号 | 0933-7741 |
| DOI | 10.1515/FORUM.2008.042 |
| 英文摘要 | We consider the minimal mass m(0) required for solutions to the mass-critical nonlinear Schrodinger (NLS) equation iu(t) + Delta u = mu vertical bar mu vertical bar(boolean AND/d)u to blow up. If m(0) is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in L(x)(2)(R(d)) is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [17], in dimensions 1, 2 and Begout and Vargas, [2], in dimensions d >= 3 for the mass-critical NLS and by Kenig and Merle, [18], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in L(x)(2)(R(d)) for the defocusing NLS in three and higher dimensions with spherically symmetric data. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000261170700006 |
| 出版者 | WALTER DE GRUYTER & CO |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6310]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Tao, Terence |
| 作者单位 | 1.Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tao, Terence,Visan, Monica,Zhang, Xiaoyi. Minimal-mass blowup solutions of the mass-critical NLS[J]. FORUM MATHEMATICUM,2008,20(5):881-919. |
| APA | Tao, Terence,Visan, Monica,&Zhang, Xiaoyi.(2008).Minimal-mass blowup solutions of the mass-critical NLS.FORUM MATHEMATICUM,20(5),881-919. |
| MLA | Tao, Terence,et al."Minimal-mass blowup solutions of the mass-critical NLS".FORUM MATHEMATICUM 20.5(2008):881-919. |
入库方式： OAI收割
来源：数学与系统科学研究院
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