RT Journal Article
T1 Global existence of a nonlinear wave equation arising from Nordström’s theory of gravitation
A1 Brauer, Uwe Richard Otto
A1 Karp, Lavi
AB 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.
PB Springer
SN 1424-3199
YR 2023
FD 2023-01-17
LK https://hdl.handle.net/20.500.14352/73013
UL https://hdl.handle.net/20.500.14352/73013
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO CRUE-CSIC agreement with Springer Nature
DS Docta Complutense
RD 10 abr 2025