Probabilistic well-posedness of the mass-critical NLS with radial data below L2(Rd)

被引：3

作者：

Hwang, Gyeongha ^{[1
]}

机构：

[1] Yeungnam Univ, Dept Math, 280 Daehak Ro, Gyongsan 38541, Gyeongbuk, South Korea

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 475卷 / 02期

关键词：

Nonlinear Schrodinger equation; Almost sure well-posedness; Strichartz estimates; Radial data; Mass-critical nonlinearity; NONLINEAR SCHRODINGER-EQUATION; DATA CAUCHY-THEORY; INVARIANT-MEASURES; WAVE-EQUATIONS; SCATTERING; DIMENSIONS;

D O I：

10.1016/j.jmaa.2019.03.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem of the mass-critical nonlinear Schrodinger equation (NLS) with radial data below L2(Rd). We prove almost sure local well-posedness along with small data global existence and scattering. Furthermore, we also derive conditional almost sure global well-posedness of the defocusing NLS under the assumption of a probabilistic a priori energy bound. The main ingredient is to establish the probabilistic radial Strichartz estimates. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1842 / 1854

页数：13

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