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Global existence of a nonlinear wave equation arising from Nordström’s theory of gravitation

Authors :
Brauer, Uwe
Karp, Lavi
Brauer, Uwe
Karp, Lavi
Publication Year :
2023

Abstract

CRUE-CSIC (Acuerdos Transformativos 2022)<br />We show global existence of classical solutions for the nonlinear Nordström theory with a source term and a cosmological constant under the assumption that the source term is small in an appropriate norm, while in some cases no smallness assumption on the initial data is required. In this theory, the gravitational field is described by a single scalar function that satisfies a certain semi-linear wave equation. We consider spatial periodic deviation from the background metric, that is why we study the semi-linear wave equation on the three-dimensional torus T3 in the Sobolev spaces Hm(T3). We apply two methods to achieve the existence of global solutions, the first one is by Fourier series, and in the second one, we write the semi-linear wave equation in a non-conventional way as a symmetric hyperbolic system. We also provide results concerning the asymptotic behavior of these solutions and, finally, a blow-up result if the conditions of our global existence theorems are not met.<br />CRUE-CSIC agreement with Springer Nature<br />Depto. de Análisis Matemático y Matemática Aplicada<br />Fac. de Ciencias Matemáticas<br />TRUE<br />pub

Details

Database :
OAIster
Notes :
application/pdf, 1424-3199, English
Publication Type :
Electronic Resource
Accession number :
edsoai.on1450537633
Document Type :
Electronic Resource