Probabilistic local wellposedness of 1D quintic NLS below L2(R)

被引：0
|
作者：
Hwang, Gyeongha [1 ]
Yoon, Haewon [2 ]
机构：
[1] Yeungnam Univ, Dept Math, 280 Daehak Ro, Gyongsan 38541, Gyeongbuk, South Korea
[2] Chung Ang Univ, Dept Math, 84 Heukseok Ro, Seoul 06974, South Korea
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Probabilistic wellposedness; Nonlinear Schrodinger equation; Bilinear Strichartz estimate; NONLINEAR SCHRODINGER-EQUATION; WELL-POSEDNESS;
D O I：
10.1016/j.jmaa.2023.127195
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem of the nonlinear Schrodinger equation i partial differential tu + partial differential x2u +/- u5 = 0 on the real line, which is L2-critical. We prove the local well-posedness of the initial value problem (IVP) for the scaling supercritical regularity regime - 10 < s < 0 in probabilistic manner. One of the main ingredient is to establish the 1 probabilistic bilinear Strichartz estimate.(c) 2023 Published by Elsevier Inc.
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