scholarly journals Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm

2011 ◽  
Vol 30 (3) ◽  
pp. 573-621 ◽  
Author(s):  
M. Keel ◽  
◽  
Tristan Roy ◽  
Terence Tao ◽  
◽  
...  
Keyword(s):  
Gordon Equation ◽  
Energy Norm ◽  
Well Posedness ◽  
Klein Gordon ◽  
Klein Gordon Equation

BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ1+1

2013 ◽  
Vol 10 (01) ◽  
pp. 1-35 ◽  
Author(s):  
TIMOTHY CANDY
Keyword(s):  
Global Existence ◽  
Gordon Equation ◽  
Well Posedness ◽  
Bilinear Estimates ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Nonlinear Dirac Equations ◽  
Klein Gordon Equation

We prove new bilinear estimates for the [Formula: see text] spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on ℝ1+1. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka and Tao, we extend the work of Tesfahun on global existence below the charge class for the Dirac–Klein–Gordon equation on ℝ1+1.

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