Geodesic
Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
Electronic journal of differential equations, Tome 2006 (2006)
Local well-posedness for Dirac-Klein-Gordon equations is proven in one space dimension, where the Dirac part belongs to $H^{-\frac{1}{4}+\epsilon}$ and the Klein-Gordon part to $H^{\frac{1}{4}-\epsilon}$ for $0 less than \epsilon less than 1/4$, and global well-posedness, if the Dirac part belongs to the charge class $L^2$ and the Klein-Gordon part to $H^k$ with $0 less than k less than 1/2$. The proof uses a null structure in both nonlinearities detected by d'Ancona, Foschi and Selberg and bilinear estimates in spaces of Bourgain-Klainerman-Machedon type.
Classification : 35Q40, 35L70
Keywords: Dirac-Klein-Gordon system, well-posedness, Fourier restriction norm method 
@article{EJDE_2006__2006__a149,
     author = {Pecher,  Hartmut},
     title = {Low regularity well-posedness for the one-dimensional {Dirac-Klein-Gordon} system},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1115.35109},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a149/}
}
TY  - JOUR
AU  - Pecher,  Hartmut
TI  - Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
JO  - Electronic journal of differential equations
PY  - 2006
VL  - 2006
UR  - http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a149/
LA  - en
ID  - EJDE_2006__2006__a149
ER  - 
%0 Journal Article
%A Pecher,  Hartmut
%T Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
%J Electronic journal of differential equations
%D 2006
%V 2006
%U http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a149/
%G en
%F EJDE_2006__2006__a149
Pecher,  Hartmut. Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a149/