ALMOST SURE WELL-POSEDNESS OF THE CUBIC NONLINEAR SCHRODINGER EQUATION BELOW L2(T)

被引：98
作者：
Colliander, James [1 ]
Oh, Tadahiro [1 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
DUKE MATHEMATICAL JOURNAL | 2012年 / 161卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
INVARIANT-MEASURES; ILL-POSEDNESS; CAUCHY; KDV; MODULATION;
D O I：
10.1215/00127094-1507400
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Cauchy problem for the 1-dimensional periodic cubic nonlinear Schrodinger (NLS) equation with initial data below L-2. In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well-posedness of the NLS equation almost surely for the initial data in the support of the canonical Gaussian measures on H-s(T) for each s > -1/3, and global well-posedness for each s> -1/2.
引用
收藏
页码：367 / 414
页数：48
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