scholarly journals Low regularity well-posedness for the 3D Klein - Gordon - Schrödinger system

2012 ◽  
Vol 11 (3) ◽  
pp. 1081-1096 ◽  
Author(s):  
Hartmut Pecher ◽  
Keyword(s):  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
Schrödinger System

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.

Global well-posedness of the fractional Klein-Gordon-Schrödinger system with rough initial data

2016 ◽  
Vol 59 (7) ◽  
pp. 1345-1366 ◽  
Author(s):  
ChunYan Huang ◽  
BoLing Guo ◽  
DaiWen Huang ◽  
QiaoXin Li
Keyword(s):  
Initial Data ◽  
Well Posedness ◽  
Klein Gordon ◽  
Rough Initial Data ◽  
Schrödinger System
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