Growth of Sobolev norms for the Maxwell–Dirac and Dirac–Klein–Gordon systems in R1+1

Article type: Research Article

Authors: Huh, Hyungjin^{; *}

Affiliations: Department of Mathematics, Chung-Ang University, Seoul, 06974, Republic of Korea. E-mail: huh@cau.ac.kr

Correspondence: [*] Corresponding author. E-mail: huh@cau.ac.kr.

Abstract: We obtain the growth of Sobolev norms of the solution to the Maxwell–Dirac equations in R1+1 by applying elementary techniques. In particular, we estimate L∞ bound of the solution by making use of a local energy conservation. The similar idea can be applied to the Dirac–Klein–Gordon equations.

Keywords: Maxwell–Dirac, Dirac–Klein–Gordon, L^∞ bound, growth of Sobolev norms

DOI: 10.3233/ASY-211700

Journal: Asymptotic Analysis, vol. 128, no. 1, pp. 103-111, 2022