Concerning the wave equation on asymptotically Euclidean manifolds

By Christopher D. Sogge, Chengbo Wang. 2008

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We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (ℝd, g), d ≥ 3, when the metric g is non-trapping and approaches the Euclidean metric like 〈x〉−ρ with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric is radial with ρ > 1 for d = 3.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/538bc654c8c66a207a1842ab759469c113b3e718