On a class of nonlinear wave equations related to the Dirac-Klein-Gordon system with generalized Yukawa interaction
type: Item
instance of: scholarly article
title: On a class of nonlinear wave equations related to the Dirac-Klein-Gordon system with generalized Yukawa interaction
zbMATH Open document ID: 1106.35091
author: Nikolaos Bournaveas
published in: Hokkaido Mathematical Journal
publication date: 2006-11-29T00:00:00Z
review text: The author studies local low regularity solutions without any smallness assumption on the data of nonlinear wave equations of the form \(\square u=u^kDu,\) where \(Du\) stands for any of the first order derivatives \(\partial_tu,\;\partial_{x_j}u,\;i=1,2,3\) with initial data \(u(0,\cdot)=f\in H^s(\mathbb{R}^{3}),\;u_t(0,\cdot)=g\in H^{s-1}(\mathbb{R}^{3}).\) Local existence for large data in both the subcritical and critical cases and global existence for small data in the critical cases are proved. The motivation of this study is the following Dirac-Klein-Gordon system with generalized Yukawa interaction \(\mathcal{D}\psi=\varphi(\overline{\psi}\psi)^{\alpha}\psi,\;\square \varphi=(\overline{\psi}\psi)^{\beta},\) to which the obtained results are applied.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 5076736
zbMATH Keywords: local low regularity solutions
zbMATH Keywords: local existence for large data
zbMATH Keywords: global existence for small data
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1285766356
OpenAlex ID: W2014967951
DOI: 10.14492/HOKMJ/1285766356
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description: scientific article; zbMATH DE number 5076736