用于周期三次NLS无条件适定性的Poincaré-Dulac规范形约化
偏微分方程分析
2011-09-07 v3 动力系统
摘要
我们实施了一个Poincaré-Dulac规范形约化的无穷迭代方案，以建立一维三次非线性薛定谔方程在C_t L^2(T)中的能量估计，而不使用任何辅助函数空间。这使我们能够构造以L^2(T)中初始数据在C_t L^2(T)中的弱解，作为经典解的极限。作为我们构造的结果，我们还证明了对于s ≥ 1/6，NLS在H^s(T)中的无条件适定性。
引用
@article{arxiv.1103.5271,
title = {Poincar\'e-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS},
author = {Zihua Guo and Soonsik Kwon and Tadahiro Oh},
journal= {arXiv preprint arXiv:1103.5271},
year = {2011}
}
备注
28 pages. In Section 3, we now use (ordered) trees for indexing multilinear terms appearing in the process (instead of assuming that the time derivative falls on the first factor as in the previous version.)