Wellposedness of some quasi-linear Schrodinger equations

被引：1
|
作者：
Chemin, Jean-Yves [1 ]
Salort, Delphine [2 ,3 ]
机构：
[1] Univ Paris 06, Lab JL Lions, UMR 7598, F-75252 Paris 05, France
[2] Univ Paris 04, Lab Biol Computat & Quantitat, UMR 7238, Paris, France
[3] Univ Paris Diderot, Inst Jacques Monod, UMR 7592, F-75205 Paris, France
来源：
SCIENCE CHINA-MATHEMATICS | 2015年 / 58卷 / 05期
基金：
美国国家科学基金会; 美国国家卫生研究院;
关键词：
quasilinear Schrodinger equation; Strichartz estimates; paradiffential calculus; stationary phase method; STRICHARTZ INEQUALITIES; CAUCHY-PROBLEM; DISPERSION;
D O I：
10.1007/s11425-015-4993-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in and belonging to the Besov space . In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the norm on the initial data.
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页码：891 / 914
页数：24
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