Differential and Integral Equations

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

Nikolaos Bournaveas and Dominic Gibbeson

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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

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35L70: Nonlinear second-order hyperbolic equations

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


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