Semilinear wave equation in Schwarzschild metric

摘要

We study the semilinear wave equation in Schwarzschild metric ((3 + 1)-dimensional space-time). First, we establish that the problem is locally well posed in Hσ for any σ ≥ 1; then we prove the blow up of the solution for every p ∈ 2~(1/2), 1 + 2~(1/2)[ and non-negative non-trivial initial data.