Sharp ill-posedness of the Dirac–Klein–Gordon system in one dimension. (March 2020)

• Record Type: Journal Article
• Authors: Machihara, Shuji; Okamoto, Mamoru
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35Q41 -- 35B30 -- 35R25; Dirac–Klein–Gordon system -- Ill-posedness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111687
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show the ill-posedness of the Cauchy problem for the Dirac–Klein–Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the regularities for which this problem is well-posed or ill-posed.