scholarly journals On global small amplitude solutions to systems of cubic nonlinear Klein–Gordon equations with different mass terms in one space dimension

2003 ◽  
Vol 192 (2) ◽  
pp. 308-325 ◽  
Author(s):  
Hideaki Sunagawa
Keyword(s):  
Small Amplitude ◽  
Space Dimension ◽  
Klein Gordon ◽  
Mass Terms ◽  
One Space Dimension

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 existence of small amplitude solutions to one-dimensional nonlinear Klein–Gordon systems with different masses

2015 ◽  
Vol 12 (04) ◽  
pp. 745-762 ◽  
Author(s):  
Donghyun Kim
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Small Amplitude ◽  
Space Dimension ◽  
Structural Condition ◽  
Cauchy Data ◽  
One Dimensional ◽  
Compactly Supported ◽  
The Cauchy Problem ◽  
Klein Gordon

We study the Cauchy problem for systems of cubic nonlinear Klein–Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate [Formula: see text] in [Formula: see text], [Formula: see text] as [Formula: see text] tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

2019 ◽  
Vol 16 (02) ◽  
pp. 313-332 ◽  
Author(s):  
Achenef Tesfahun
Keyword(s):  
Space Dimension ◽  
Higher Order ◽  
Sobolev Norms ◽  
Klein Gordon ◽  
One Space Dimension

We study the growth-in-time of higher order Sobolev norms of solutions to the Dirac–Klein–Gordon (DKG) equations in one space dimension. We show that these norms grow at most polynomially-in-time. The main ingredients in the proof are the upside-down [Formula: see text]-method which was introduced by Colliander, Keel, Staffilani, Takaoka and Tao, and bilinear null-form estimates.

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