Geodesic
Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Pecher, Hartmut},
     title = {Low regularity well-posedness for the one-dimensional {Dirac-Klein-Gordon} system},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a149/}
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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/