Almost Sure Well-Posedness of Fractional Schrodinger Equations with Hartree Nonlinearity

被引：1

作者：

Hwang, Gyeongha ^{[1
]}

机构：

[1] Natl Taiwan Univ, Natl Ctr Theoret Sci, 1,Sec 4,Roosevelt Rd, Taipei 10617, Taiwan

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2018年 / 54卷 / 01期

关键词：

Nonlinear Schrodinger equation; fractional Schrodinger equation; Hartree non linearity; almost sure well-posedness; WAVE EQUATION; INSTABILITY; SCATTERING; REGULARITY;

D O I：

10.4171/PRIMS/54-1-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a Cauchy problem of an energy-critical fractional Schrodinger equation with Hartree nonlinearity below the energy space. Using randomization of functions on R-d associated with the Wiener decomposition, we prove that the Cauchy problem is almost surely locally well posed. Our result includes the Hartree Schrodinger equation (alpha = 2).

引用

页码：1 / 44

页数：44

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