The Cubic Dirac Equation: Small Initial Data in

被引：0

作者：

Bejenaru, Ioan ^{[1
]}

Herr, Sebastian ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2015年 / 335卷 / 01期

关键词：

NONLINEAR KLEIN-GORDON; GLOBAL EXISTENCE; WAVE MAPS; TIME DECAY; WELL-POSEDNESS; SCHRODINGER; REGULARITY; SCATTERING; DIMENSIONS; ENERGY;

D O I：

10.1007/s00220-014-2164-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish global well-posedness and scattering for the cubic Dirac equation for small data in the critical space . The main ingredient is obtaining a sharp end-point Strichartz estimate for the Klein-Gordon equation. In a classical sense this fails and it is related to the failure of the endpoint Strichartz estimate for the wave equation in space dimension three. In this paper, systems of coordinate frames are constructed in which endpoint Strichartz estimates are recovered and energy estimates are established.

引用

页码：43 / 82

页数：40

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