## Differential and Integral Equations

### Low regularity global solutions of the Dirac-Klein-Gordon equations in one space dimension

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 2 (2006), 211-222.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356050525

Mathematical Reviews number (MathSciNet)
MR2194504

Zentralblatt MATH identifier
1212.35269

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics

#### Citation

Bournaveas, Nikolaos; Gibbeson, Dominic. Low regularity global solutions of the Dirac-Klein-Gordon equations in one space dimension. Differential Integral Equations 19 (2006), no. 2, 211--222. https://projecteuclid.org/euclid.die/1356050525