Abstract
We prove global existence for the Dirac-Klein-Gordon equations in one space dimension with $\psi\in L^2$ (charge class) and $\phi\in H^{1/4}$. This improves the global existence result of Fang [7] by $1/4 + \epsilon$ derivatives in $\phi$. The proof relies on bilinear estimates for solutions of the Dirac equation and a decomposition of the spinor field into `left' and `right' spinors.
Citation
Nikolaos Bournaveas. Dominic Gibbeson. "Low regularity global solutions of the Dirac-Klein-Gordon equations in one space dimension." Differential Integral Equations 19 (2) 211 - 222, 2006. https://doi.org/10.57262/die/1356050525
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