论文标题
改善了近渐近平坦的空位（包括黑洞空位）的质波方程的衰减。
Improved decay for quasilinear wave equations close to asymptotically flat spacetimes including black hole spacetimes
论文作者
论文摘要
We study the quasilinear wave equation $\Box_{g}ϕ=0$ where the metric $g = g(ϕ,t,x)$ is close to and asymptotically approaches $g(0,t,x)$, which equals the Schwarzschild metric or a Kerr metric with small angular momentum, as time tends to infinity.在仅在度量系数上的弱假设下，我们证明解决方案$ ϕ $的衰减率提高了。此速率的结果是，对于有限的$ | x | $，我们有可集成的衰减率$ | ϕ（t，x）| \ le ct^{ - 1- \ min（δ，1）} $，其中$δ> 0 $是质锥附近的衰减的参数，是准线性最慢的终止项的系数。 We also obtain the same aforementioned pointwise decay rates for the quasilinear wave equation $(\Box_{\tilde g} + B^α(t,x)\partial_α+ V(t,x))ϕ=0$ with a more general asymptotically flat metric $\tilde g = \tilde g(ϕ,t,x)$ and with other time-dependent asymptotically平较低订单条款。
We study the quasilinear wave equation $\Box_{g}ϕ=0$ where the metric $g = g(ϕ,t,x)$ is close to and asymptotically approaches $g(0,t,x)$, which equals the Schwarzschild metric or a Kerr metric with small angular momentum, as time tends to infinity. Under only weak assumptions on the metric coefficients, we prove an improved pointwise decay rate for the solution $ϕ$. One consequence of this rate is that for bounded $|x|$, we have the integrable decay rate $|ϕ(t,x)| \le Ct^{-1-\min(δ,1)}$ where $δ>0$ is a parameter governing the decay, near the light cone, of the coefficient of the slowest-decaying term in the quasilinearity. We also obtain the same aforementioned pointwise decay rates for the quasilinear wave equation $(\Box_{\tilde g} + B^α(t,x)\partial_α+ V(t,x))ϕ=0$ with a more general asymptotically flat metric $\tilde g = \tilde g(ϕ,t,x)$ and with other time-dependent asymptotically flat lower order terms.
