WELL-POSEDNESS AND ILL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE MAXWELL DIRAC SYSTEM IN 1+1 SPACE TIME DIMENSIONS

被引：0

作者：

Okamoto, Mamoru ^{[1
]}

机构：

[1] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2013年 / 18卷 / 1-2期

关键词：

LOCAL EXISTENCE; NULL STRUCTURE; EQUATIONS; REGULARITY; FORMS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We completely determine the range of Sobolev regularity for the Maxwell-Dirac system in 1 + 1 space time dimensions to be well-posed locally in the case that the initial data of the Dirac part regularity is of L-2. The well-posedness follows from the standard energy 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：179 / 199

页数：21

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