scholarly journals On global well-posedness and scattering for the massive Dirac–Klein–Gordon system

2017 ◽  
Vol 19 (8) ◽  
pp. 2445-2467 ◽  
Author(s):  
Ioan Bejenaru ◽  
Sebastian Herr
Keyword(s):  
Well Posedness ◽  
Klein Gordon

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.

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

scholarly journals GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX

2009 ◽  
Vol 06 (03) ◽  
pp. 631-661 ◽  
Author(s):  
ACHENEF TESFAHUN
Keyword(s):  
Sobolev Spaces ◽  
Well Posedness ◽  
Dirac Spinor ◽  
Negative Index ◽  
Main Ingredient ◽  
Time Estimates ◽  
The Cauchy Problem ◽  
Klein Gordon ◽  
Positive Index ◽  
Well Posed

We prove that the Cauchy problem for the Dirac–Klein–Gordon system of equations in 1D is globally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor and positive index for the scalar field. The main ingredient in the proof is the theory of "almost conservation law" and "I-method" introduced by Colliander, Keel, Staffilani, Takaoka, and Tao. Our proof also relies on the null structure in the system, and bilinear space–time estimates of Klainerman–Machedon type.

scholarly journals Local well-posedness of the two-dimensional Dirac–Klein–Gordon equations in Fourier–Lebesgue spaces

2020 ◽  
Vol 17 (04) ◽  
pp. 785-796
Author(s):  
Hartmut Pecher
Keyword(s):  
Classical Case ◽  
Well Posedness ◽  
Two Dimensional ◽  
Null Condition ◽  
Lebesgue Spaces ◽  
Klein Gordon ◽  
Two Space Dimensions

The local well-posedness problem is considered for the Dirac–Klein–Gordon system in two space dimensions for data in Fourier–Lebesgue spaces [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d’Ancona et al. in the classical case [Formula: see text]. Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.

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