We consider the Cauchy problem for massless Dirac–Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be extended via analogous methods to Dirac–Higgs–Yang–Mills theories.
Mots clés : Maxwell–Dirac equation, Initial value problem, Cauchy problem, Conformal compactification, Symmetric hyperbolic systems
@article{AIHPC_2018__35_6_1645_0, author = {Ginoux, Nicolas and M\"uller, Olaf}, title = {Global solvability of massless {Dirac{\textendash}Maxwell} systems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1645--1654}, publisher = {Elsevier}, volume = {35}, number = {6}, year = {2018}, doi = {10.1016/j.anihpc.2018.01.005}, mrnumber = {3846239}, zbl = {1403.35252}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.005/} }
TY - JOUR AU - Ginoux, Nicolas AU - Müller, Olaf TI - Global solvability of massless Dirac–Maxwell systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 1645 EP - 1654 VL - 35 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.005/ DO - 10.1016/j.anihpc.2018.01.005 LA - en ID - AIHPC_2018__35_6_1645_0 ER -
%0 Journal Article %A Ginoux, Nicolas %A Müller, Olaf %T Global solvability of massless Dirac–Maxwell systems %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 1645-1654 %V 35 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.005/ %R 10.1016/j.anihpc.2018.01.005 %G en %F AIHPC_2018__35_6_1645_0
Ginoux, Nicolas; Müller, Olaf. Global solvability of massless Dirac–Maxwell systems. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1645-1654. doi : 10.1016/j.anihpc.2018.01.005. http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.005/
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