Growth of Sobolev norms for the Maxwell–Dirac and Dirac–Klein–Gordon systems in R 1 + 1

DOI10.3233/ASY-211700OpenAlexW3157351221MaRDI QIDQ5061580

Hyungjin Huh

Publication date: 14 March 2022

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-211700

zbMATH Keywords

\(L^\infty\) boundgrowth of Sobolev normsDirac-Klein-GordonMaxwell-Dirac

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Summability and bases in topological vector spaces (46A35) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

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• Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field
• Well-posedness and ill-posedness of the Cauchy problem for the Maxwell-Dirac system in \(1+1\) space time dimensions
• Global solutions to Gross-Neveu equation
• Global solution to Maxwell-Dirac equations in \(1+1\) dimensions
• Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
• BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ¹⁺¹
• Global charge solutions of Maxwell–Dirac equations in \mathbb {R}^{1+1}
• GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX
• Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

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