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We study the linear wave equation □ 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 τ = 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 expansion of ru in terms of 1/ r as r → ∞.

Asymptotics for null-timelike boundary problems for general linear wave equations