Asymptotics for Null-timelike Boundary Problems for General Linear Wave Equations

Abstract

We study the linear wave equation ${\square }_{g}u=0$ in Bondi-Sachs coordinates, for an asymptotically flat Lorentz metric $g$. We consider the null-timelike boundary problem, where an initial value is given on the null surface $\tau =0$ and a boundary value on the timelike surface $r=r_0$. We obtain spacetime $H^p$-estimates of $ru$ for $r>r_0$ and derive an asymptotic exapnsion of $ru$ in terms of $1/r$ as $r\to \infty$.

Cited by in corpus (1)

• The Null-Timelike Boundary Problems of Linear Wave Equations in Asymptotically Anti-de Sitter Space