LOW REGULARITY LOCAL WELL-POSEDNESS FOR THE MAXWELL-KLEIN-GORDON EQUATIONS IN LORENZ GAUGE

被引：0

作者：

Pecher, Hartmut ^{[1
]}

机构：

[1] Berg Univ Wuppertal, Fachbereich Math & Nat Wissensch, D-42097 Wuppertal, Germany

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2014年 / 19卷 / 3-4期

关键词：

4-DIMENSIONAL MINKOWSKI SPACE; WAVE-SOBOLEV SPACES; MILLS-HIGGS FIELDS; GLOBAL EXISTENCE; NULL STRUCTURE; FINITE-ENERGY; SYSTEM; DIMENSIONS; NORM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in two and three space dimensions is locally well-posed for low regularity data without finite energy. The result relies on the null structure for the main bilinear terms, which was shown to be not only present in Coulomb gauge but also in Lorenz gauge by Selberg and Tesfahun, who proved global well-posedness for finite energy data in three space dimensions. This null structure is combined with product estimates for wave-Sobolev spaces given systematically by d'Ancona, Foschi and Selberg.

引用

页码：359 / 386

页数：28

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