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

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.