Concerning the Wave Equation on Asymptotically Euclidean Manifolds
نویسندگان
چکیده
We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 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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The Semilinear Wave Equation on Asymptotically Euclidean Manifolds
We consider the quadratically semilinear wave equation on (R, g), d ≥ 3. The metric g is non-trapping and approaches the Euclidean metric like 〈x〉. Using Mourre estimates and the Kato theory of smoothness, we obtain, for ρ > 0, a Keel–Smith–Sogge type inequality for the linear equation. Thanks to this estimate, we prove long time existence for the nonlinear problem with small initial data for ρ...
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