Existence of global solutions to nonlinear massless Dirac system and wave equation with small data
type: Item
instance of: scholarly article
title: Existence of global solutions to nonlinear massless Dirac system and wave equation with small data
zbMATH Open document ID: 0945.35075
author: Nikolay Tzvetkov
published in: Tsukuba Journal of Mathematics
publication date: 2000-01-04T00:00:00Z
review text: This paper deals with the Cauchy problem for a semilinear massless Dirac system. The author proves the existence of a global solution assuming the initial data to be sufficiently small. The approach here used is based on the conservation law of charge and on Sobolev type weighted estimates for the spinor field. Similar methods enable the author to prove global existence for the Cauchy problem for the wave equation, with nonlinearity in the right-hand side \(|u_t|^\nu\), \(\nu> 2\) in 3 space dimensions. This way he generalizes some results of T. Sideris and H. Takamura where the case of spherically symmetric initial data was considered only.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 1383407
zbMATH Keywords: Dirac system
zbMATH Keywords: Cauchy problem
zbMATH Keywords: global existence
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163480
OpenAlex ID: W2141215763
DOI: 10.21099/TKBJM/1496163480
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description: scientific article; zbMATH DE number 1383407