Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

Stefano Pasquali

doi:10.1063/1.4994969

Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

Analysis of PDEs 2018-02-14 v5 Mathematical Physics math.MP

Authors: Stefano Pasquali

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Abstract

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$ , which however has to belong to a set of large measure.

Keywords

nonlinear Klein-Gordon equation nonrelativistic limit almost global existence convolution potential small norm solutions long-time behavior

Cite

@article{arxiv.1703.01618,
  title  = {Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit},
  author = {Stefano Pasquali},
  journal= {arXiv preprint arXiv:1703.01618},
  year   = {2018}
}

Comments

Some typos corrected

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