JournalsaihpcVol. 38, No. 6pp. 1681–1702

A normalized solitary wave solution of the Maxwell-Dirac equations

  • Margherita Nolasco

    Dipartimento di Ingegneria e Scienze dell'informazione e Matematica, Università dell'Aquila, via Vetoio, Loc. Coppito, 67010 L'Aquila (AQ), Italy
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Abstract

We prove the existence of a -normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.

Cite this article

Margherita Nolasco, A normalized solitary wave solution of the Maxwell-Dirac equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 6, pp. 1681–1702

DOI 10.1016/J.ANIHPC.2020.12.006