A REMARK ON NORM INFLATION FOR NONLINEAR SCHRODINGER EQUATIONS

被引：34
|
作者：
Kishimoto, Nobu [1 ]
机构：
[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2019年 / 18卷 / 03期
关键词：
Nonlinear Schrodinger equations; ill-posedness; norm inflation; power series expansion; negative Sobolev spaces; ILL-POSEDNESS; WELL-POSEDNESS; GEOMETRIC OPTICS; CAUCHY-PROBLEM; REGULARITY; INSTABILITY; NLS; BOUSSINESQ; BOUNDS;
D O I：
10.3934/cpaa.2019067
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider semilinear Schrodinger equations with nonlinearity that is a polynomial in the unknown function and its complex conjugate, on R-d or on the torus. Norm inflation (ill-posedness) of the associated initial value problem is proved in Sobolev spaces of negative indices. To this end, we apply the argument of Iwabuchi and Ogawa (2012), who treated quadratic nonlinearities. This method can be applied whether the spatial domain is non-periodic or periodic and whether the nonlinearity is gauge/scale-invariant or not.
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页码：1375 / 1402
页数：28
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