Global existence of a nonlinear wave equation arising from Nordström's theory of gravitation release_ectbg4djrvgrrkvtp46yuqmdey

by Uwe Brauer, Lavi Karp

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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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Type  article
Stage   submitted
Date   2019-12-20
Version   v2
Language   en ?
arXiv  1912.03643v2
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