The nonlinear Schrodinger equation with combined power-type nonlinearities
文献类型：期刊论文
| 作者 | Tao, Terence; Visan, Monica; Zhang, Xiaoyi |
| 刊名 | COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2007 |
| 卷号 | 32期号:7-9页码:1281-1343 |
| 关键词 | energy-critical mass-critical nonlinear Schrodinger equation well-posedness |
| ISSN号 | 0360-5302 |
| DOI | 10.1080/03605300701588805 |
| 英文摘要 | We undertake a comprehensive study of the nonlinear Schrodinger equation iu(t) + Delta u = lambda(1)vertical bar u vertical bar(p1)u + lambda(2 vertical bar)u vertical bar(p2)u, where u(t, x) is a complex-valued function in spacetime IRt x IRx", lambda(1), and lambda(2) are nonzero real constants, and 0 < p(1) < p(2) <= 4/n-2 We address questions related to local and global well-posedness, finite time blowup, and asymptotic behaviour. Scattering is considered both in the energy space H-1(IRn) and in the pseudoconformal space Sigma : = {f is an element of H-1 (IRn); xf is an element of L-2 (IRn)}. Of particular interest is the case when both nonlinearities are defocusing and correspond to the L-x(2)-critical, respectively H-x(1)-critical NLS, that is, lambda(1),lambda(2) > 0 and p(1) = 4/n, p(2) = 4/n-2. The results at the endpoint p(1) = 4/n are conditional on a conjectured global existence and spacetime estimate for the L-x(2)-critical nonlinear Schrodinger equation, which has been verified in dimensions n >= 2 for radial data in Tao et al. (to appear a,b) and Killip et al. (preprint). As an off-shoot of our analysis, we also obtain a new, simpler proof of scattering in H-x(1) for solutions to the nonlinear Schrodinger equation iu(t) + Delta u = vertical bar u vertical bar(p)u, with 4/n < p < 4/n-2 which was first obtained by Ginibre and Velo (1985). |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000250012900013 |
| 出版者 | TAYLOR & FRANCIS INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5246]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Visan, Monica |
| 作者单位 | 1.Inst Adv Study, Sch Math, Princeton, NJ 08540 USA 2.Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tao, Terence,Visan, Monica,Zhang, Xiaoyi. The nonlinear Schrodinger equation with combined power-type nonlinearities[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2007,32(7-9):1281-1343. |
| APA | Tao, Terence,Visan, Monica,&Zhang, Xiaoyi.(2007).The nonlinear Schrodinger equation with combined power-type nonlinearities.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,32(7-9),1281-1343. |
| MLA | Tao, Terence,et al."The nonlinear Schrodinger equation with combined power-type nonlinearities".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 32.7-9(2007):1281-1343. |
入库方式： OAI收割
来源：数学与系统科学研究院
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