Global existence of a nonlinear wave equation arising from Nordström's theory of gravitation release_rev_7a4ec96f-711d-4e94-87a0-5222a42f862a

by Uwe Brauer, Lavi Karp

Released as a article .

2019  

Abstract

We show global existence of classical solutions for the nonlinear Nordstr\"om theory with a source term and a cosmological constant under the assumption that the source term is small in an appropriate norm, with periodic initial data. That is why we study these equations on the three-dimensional torus in the Sobolev spaces. In some cases, the initial data have to be small in an appropriate norm. In order to achieve that the solutions decay asymptotically to zero, we are forced to use also the homogeneous Sobolev spaces. Moreover, we provide a blow-up result if the conditions of our global existence theorem are not met. We use Fourier series techniques and the theory of symmetric hyperbolic systems to achieve our results.
In text/plain format

Type  article
Stage   submitted
Date   2019-12-20
Version   v2
Language   en ?
arXiv  1912.03643v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Revision

This is a specific, static metadata record, not necessarily linked to any current entity in the catalog.

Catalog Record
Revision: 7a4ec96f-711d-4e94-87a0-5222a42f862a
API URL: JSON