WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN-SIMONS-DIRAC SYSTEM IN TWO DIMENSIONS

被引：5

作者：

Okamoto, Mamoru ^{[1
]}

机构：

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

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2013年 / 10卷 / 04期

关键词：

Well-posedness; Dirac equation; null structure; OPTIMAL LOCAL REGULARITY; WAVE-SOBOLEV SPACES; NULL STRUCTURE; EQUATIONS;

D O I：

10.1142/S0219891613500276

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem associated with the Chern-Simons-Dirac system in R1+2. Using gauge invariance, we reduce the Chern-Simons-Dirac system to a Dirac equation and we uncover the null structure of this Dirac equation. Next, relying on null structure estimates, we establish that the Cauchy problem associated with this Dirac equation is locally-in-time well-posed in the Sobolev space H-s for all s > 1/4. Our proof uses modified L-4-type estimates.

引用

页码：735 / 771

页数：37

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