Concerning the Wave equation on Asymptotically Euclidean Manifolds

Abstract

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $({\mathbb{R}}^d,\mathfrak{g})$, $d\ge 3$, when metric $\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $x^{-\rho }$ with $\rho >0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\rho >1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\rho >0$ for $d=3$.

Final version. To appear in Journal d'Analyse Mathematique

References in corpus (1)

• Weighted Strichartz Estimates with Angular Regularity and their Applications

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• The Glassey conjecture on asymptotically flat manifolds
• Concerning the Strauss conjecture on asymptotically Euclidean manifolds
• Pointwise decay for the wave equation on nonstationary spacetimes
• A Vector Field Method for Non-Trapping, Radiating Spacetimes
• The weak null condition on Kerr backgrounds