scholarly journals Local well-posedness for low regularity data for the higher dimensional Maxwell-Klein-Gordon system in Lorenz gauge

2018 ◽  
Vol 59 (10) ◽  
pp. 101503
Author(s):  
Hartmut Pecher
Keyword(s):  
Well Posedness ◽  
Low Regularity ◽  
Higher Dimensional ◽  
Klein Gordon ◽  
Lorenz Gauge

scholarly journals LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION

2008 ◽  
Vol 10 (02) ◽  
pp. 181-194 ◽  
Author(s):  
SIGMUND SELBERG ◽  
ACHENEF TESFAHUN
Keyword(s):  
Dirac Operator ◽  
Space Dimension ◽  
One Dimension ◽  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
One Space Dimension

We extend recent results of Machihara and Pecher on low regularity well-posedness of the Dirac–Klein–Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain–Klainerman–Machedon spaces.

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