SOLUTIONS TO NONLINEAR HIGHER ORDER SCHRODINGER EQUATIONS WITH SMALL INITIAL DATA ON MODULATION SPACES

被引：0
|
作者：
Kato, Tomoya [1 ]
机构：
[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan
来源：
ADVANCES IN DIFFERENTIAL EQUATIONS | 2016年 / 21卷 / 3-4期
关键词：
UNIMODULAR FOURIER MULTIPLIERS; OSCILLATORY INTEGRALS; HYPERBOLIC-EQUATIONS; CONVEX HYPERSURFACES; CAUCHY-PROBLEM;
D O I：
暂无
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 for the non-linear higher order Schrodinger equations on modulation spaces M-p,q(s) and show the existence of a unique global solution by using integrability of time decay factors of time decay estimates. As a result, we are able to deal with wider classes of a nonlinearity and a solution space. Moreover, we study time decay estimates of a semi group e(it phi(root-Delta/)) with a polynomial symbol phi. Considering multiplicities of critical points and inflection points of phi carefully, we have time decay estimates with better time decay rate.
引用
收藏
页码：201 / 234
页数：34
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