On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data
文献类型：期刊论文
| 作者 | Li, Dong1; Zhang, Xiaoyi1,2 |
| 刊名 | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2010-12-01 |
| 卷号 | 7期号:4页码:345-373 |
| 关键词 | Focusing mass critical NLS Sobolev regularity scattering conjecture |
| ISSN号 | 1548-159X |
| 英文摘要 | In this paper, we consider the six-dimensional focusing mass critical NLS: iu(t) + Delta u = -vertical bar u vertical bar(2/3) u with splitting-spherical initial data u(0)(x(1), ... x(6)) = u(0)(root x(1)(2) + x(2)(2) + x(3)(2), root x(4)(2) + x(5)(2) + x(6)(2)). we prove that any finite mass solution which is almost periodic modulo scaling in both time directions must have Sobolev regularity H(x)(1+). Moreover, the kinetic energy of the solution is localized around the spatial origin uniformly in time. As important applications of the results, we prove the scattering conjecture for solutions with mass smaller than that of the ground state. We also prove that any two-way non-scattering solution must be global and coincides with the solitary wave up to symmetries. Here the ground state is the unique positive, radial solution of the nonlinear elliptic equation Delta Q - Q + Q(5/3) = 0. To prove the smoothness of the solution, we use a new local iteration scheme which first appears in [19]. |
| 资助项目 | Mathematics Department of University of Iowa ; NSF[090832] ; Alfred P. Sloan Research Fellowship |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000287554600004 |
| 出版者 | INT PRESS BOSTON, INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9508]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Li, Dong |
| 作者单位 | 1.Univ Iowa, Dept Math, Iowa City, IA 52246 USA 2.Acad Math & Syst Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Dong,Zhang, Xiaoyi. On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,2010,7(4):345-373. |
| APA | Li, Dong,&Zhang, Xiaoyi.(2010).On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data.DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,7(4),345-373. |
| MLA | Li, Dong,et al."On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data".DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 7.4(2010):345-373. |
入库方式： OAI收割
来源：数学与系统科学研究院
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