English

Decay rates for cubic and higher order nonlinear wave equations on asymptotically flat spacetimes

Analysis of PDEs 2022-07-22 v1

Abstract

In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent spacetimes. We assume that the solution to the linear equation (rather than the nonlinear equation) satisfies a weaker form of the standard integrated local energy decay, or Morawetz, estimate. For nonlinearities with a total derivative structure, we prove better pointwise decay rates.

Keywords

Cite

@article{arxiv.2207.10280,
  title  = {Decay rates for cubic and higher order nonlinear wave equations on asymptotically flat spacetimes},
  author = {Shi-Zhuo Looi},
  journal= {arXiv preprint arXiv:2207.10280},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2205.13197