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
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.
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1912.03643v2
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