论文标题
立方体和高阶非线性波方程的衰减率在渐近平面上
Decay rates for cubic and higher order nonlinear wave equations on asymptotically flat spacetimes
论文作者
论文摘要
在本文中，我们证明了在渐近平坦且依赖时间依赖时间的时间上的立方和高阶非线波方程（包括准线波方程）的衰减率。我们假设对线性方程（而不是非线性方程）的解决方案满足了标准综合局部能量衰减或Morawetz估算的较弱形式。对于具有总导数结构的非线性，我们证明了更好的点衰减率。
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.
