## Differential and Integral Equations

### Global charge class solutions of the Dirac-Klein-Gordon equations in one space dimension

#### Abstract

In a recent paper [3] we proved global well posedness for the Dirac-Klein-Gordon equations with Yukawa interaction in $1+1$ dimensions with initial data $\psi_{0}\in L^2(\mathbb R)$, $(\phi_{0},\phi_{1})\in {H^{r}(\mathbb R)} \times {H^{r-1}(\mathbb R)}$, where $r\in[1/4,1]$, $r\neq 1/2$. In this paper we use a new null form estimate to prove global well posedness for the more difficult case $r=1/2$.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 9 (2006), 1001-1018.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050329

Mathematical Reviews number (MathSciNet)
MR2262093

Zentralblatt MATH identifier
1212.35284

#### Citation

Bournaveas, Nikolaos; Gibbeson, Dominic. Global charge class solutions of the Dirac-Klein-Gordon equations in one space dimension. Differential Integral Equations 19 (2006), no. 9, 1001--1018. https://projecteuclid.org/euclid.die/1356050329