A normalized solitary wave solution of the Maxwell-Dirac equations
Nolasco, Margherita1
1 Dipartimento di Ingegneria e Scienze dell'informazione e Matematica, Università dell'Aquila, via Vetoio, Loc. Coppito, 67010 L'Aquila (AQ), Italy
Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1681-1702.
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We prove the existence of a L2-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.

Reçu le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.12.006
Classification : 49S05, 81V10, 35Q60, 35Q51
Mots-clés : Maxwell-Dirac equations, Solitary waves, Variational methods
Nolasco, Margherita 1

1 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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Nolasco, Margherita. A normalized solitary wave solution of the Maxwell-Dirac equations. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1681-1702. doi : 10.1016/j.anihpc.2020.12.006. http://www.numdam.org/articles/10.1016/j.anihpc.2020.12.006/

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Research partially supported by MIUR grant PRIN 2015 2015KB9WPT, “Variational methods, with applications to problems in mathematical physics and geometry”.