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



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Brauer, Uwe and Karp, Lavi (2023) Global existence of a nonlinear wave equation arising from Nordström’s theory of gravitation. Journal of Evolution Equations, 23 (1). ISSN 1424-3199

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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.

Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Global existence, Nordström theory, Semi-linear wave equation, Homogeneous Sobolev spaces, Hyperbolic symmetric systems, Energy estimates
Subjects:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Algebraic geometry
ID Code:76749
Deposited On:21 Feb 2023 13:53
Last Modified:22 Feb 2023 16:01

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