Well-posedness of the Cauchy problem for the Maxwell-Dirac system in one space dimension

被引：0

作者：

Okamoto, Mamoru ^{[1
]}

机构：

[1] Kyoto Univ, Sakyo Ku, Kyoto 6068502, Japan

来源：

NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 64卷

关键词：

Maxwell-Dirac system; null structure; local well-poseness; LOCAL EXISTENCE; NULL STRUCTURE; EQUATIONS; REGULARITY; FORMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the range of Sobolev regularity for the Maxwell-Dirac system in 1 + 1 space time dimensions to be well-posed locally. The well-posedness follows from the null form estimates. Outside the range for the well-posedness, we show either the flow map is not continuous or not twice differentiable at zero.

引用

页码：497 / 505

页数：9

共 19 条

[1]

[Anonymous], 1976, GRUNDLEHREN MATH WIS

[2]

Bourgain J., 1993, Geom. Funct. Anal., V3, P107

[3] Local existence for the Maxwell-Dirac equations in three space dimensions [J].