Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
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DOI：
10.1016/j.jmaa.2020.124654
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发表时间：
2019-11
影响因子：
1.3
通讯作者：
Xing Cheng;Zehua Zhao;Jiqiang Zheng
中科院分区：
文献类型：
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作者：
Xing Cheng;Zehua Zhao;Jiqiang Zheng
本文利用巴伦[1]基于Bourgain-Demeter l2解耦方法[3]提出的波导尺度不变的Schr hartz估计，对波导能量临界非线性Schr dinger方程在三维和四维时的适定性结果给出了统一而简单的处理. Killip-Visan [30]讨论并证明了环面类似物。最后，对波导装置下大数据NLS的长时间动力学特性进行了评述。
In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is recently developed by Barron [1] based on Bourgain-Demeter l 2 decoupling method [3] to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schrödinger equation on waveguide when the whole dimension is three and four. The tori analogue is discussed and proved by Killip-Visan [30]. At last, we give some comments on long time dynamics of NLS with large data in the setting of waveguide.