no. 6
On the Majorana condition for nonlinear Dirac systems
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1707-1717.

For arbitrarily large initial data in an open set defined by an approximate Majorana condition, global existence and scattering results for solutions to the Dirac equation with Soler-type nonlinearity and the Dirac–Klein–Gordon system in critical spaces in spatial dimension three are established.

DOI : 10.1016/j.anihpc.2018.02.001
Classification : 42B37, 35Q41
Mots clés : Cubic Dirac equation, Dirac–Klein–Gordon system, Global existence, Scattering, Majorana condition 
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Candy, Timothy; Herr, Sebastian. On the Majorana condition for nonlinear Dirac systems. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1707-1717. doi : 10.1016/j.anihpc.2018.02.001. http://www.numdam.org/articles/10.1016/j.anihpc.2018.02.001/

[1] Bachelot, Alain Nonlinear Hyperbolic Problems, Lecture Notes in Math., Volume vol. 1402, Springer, Berlin (1989), pp. 99–113 (Bordeaux, 1988 MR 1033278) | DOI | MR | Zbl

[2] Bachelot, Alain Workshop on Hyperbolic Systems and Mathematical Physics, Port. Math., Volume 46 (1989) no. suppl., pp. 455–473 (Lisbon, 1988 MR 1080766) | MR | Zbl

[3] Bejenaru, Ioan; Herr, Sebastian The cubic Dirac equation: small initial data in H1(R3) , Commun. Math. Phys., Volume 335 (2015) no. 1, pp. 43–82 (MR 3314499) | MR | Zbl

[4] Bejenaru, Ioan; Herr, Sebastian The cubic Dirac equation: small initial data in H12(R2) , Commun. Math. Phys., Volume 343 (2016) no. 2, pp. 515–562 (MR 3477346) | MR | Zbl

[5] Bejenaru, Ioan; Herr, Sebastian On global well-posedness and scattering for the massive Dirac–Klein–Gordon system, J. Eur. Math. Soc., Volume 19 (2017) no. 8, pp. 2445–2467 (MR 3668064) | MR | Zbl

[6] Bjorken, James D.; Drell, Sidney D. Relativistic Quantum Mechanics, McGraw-Hill Book Co., New York, Toronto, London, 1964 (MR 0187641) | MR

[7] Bournaveas, Nikolaos; Candy, Timothy Global well-posedness for the massless cubic Dirac equation, Int. Math. Res. Not., Volume 2016 (2016) no. 22, pp. 6735–6828 (MR 3632067) | MR | Zbl

[8] Candy, Timothy; Herr, Sebastian Conditional large data scattering results for the Dirac–Klein–Gordon system | arXiv | Zbl

[9] Candy, Timothy; Herr, Sebastian Transference of bilinear restriction estimates to quadratic variation norms and the Dirac–Klein–Gordon system, Anal. PDE (2018) (in press) | arXiv | MR | Zbl

[10] Chadam, John M.; Glassey, Robert T. On certain global solutions of the Cauchy problem for the (classical) coupled Klein–Gordon–Dirac equations in one and three space dimensions, Arch. Ration. Mech. Anal., Volume 54 (1974), pp. 223–237 MR 0369952 (51 #6181) | MR | Zbl

[11] D'Ancona, Piero; Okamoto, Mamoru On the cubic Dirac equation with potential and the Lochak–Majorana condition, J. Math. Anal. Appl., Volume 456 (2017), pp. 1203–1237 | MR | Zbl

[12] Elliott, Steven R.; Franz, Marcel Colloquium: Majorana fermions in nuclear, particle, and solid-state physics, Rev. Mod. Phys., Volume 87 (2015), pp. 137–163 | MR

[13] Lochak, Georges Wave equation for a magnetic monopole, Int. J. Theor. Phys., Volume 24 (1985) no. 10, pp. 1019–1050 | MR

[14] Majorana, Ettore Teoria simmetrica dell'elettrone e del positrone, Nuovo Cimento, Volume 14 (1937) no. 4, pp. 171–184 | Zbl

[15] Ozawa, Tohru; Yamauchi, Kazuyuki Structure of Dirac matrices and invariants for nonlinear Dirac equations, Differ. Integral Equ., Volume 17 (2004) no. 9–10, pp. 971–982 (MR 2082456) | MR | Zbl

[16] Thaller, Bernd The Dirac Equation, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1992 (MR 1219537) | MR | Zbl

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