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Concerning the wave equation on asymptotically Euclidean manifolds

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Christopher D. Sogge & Chengbo Wang

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  1. Christopher D. Sogge
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  2. Chengbo Wang
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Correspondence to Christopher D. Sogge.

Additional information

The first author was supported by the National Science Foundation.

The second author was supported in part by NSFC 10871175.

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Sogge, C.D., Wang, C. Concerning the wave equation on asymptotically Euclidean manifolds. JAMA 112, 1–32 (2010). https://doi.org/10.1007/s11854-010-0023-2

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  • DOI: https://doi.org/10.1007/s11854-010-0023-2

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