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The semilinear wave equation on asymptotically euclidean manifolds
Language
en
Article de revue
This item was published in
Comm. Partial Differential Equations. 2010, vol. 35, n° 1, p. 23-67
English Abstract
We consider the quadratically semilinear wave equation on R^d, d>=3, equipped with a Riemannian metric. This metric is non-trapping and approaches the Euclidean metric polynomially at infinity. Using Mourre estimates and ...Read more >
We consider the quadratically semilinear wave equation on R^d, d>=3, equipped with a Riemannian metric. This metric is non-trapping and approaches the Euclidean metric polynomially at infinity. Using Mourre estimates and the Kato theory of smoothness, we obtain a Keel-Smith-Sogge type inequality for the linear equation. Thanks to this estimate, we prove long time existence (d=3) and global existence (d>3) for the nonlinear problem with small initial data.Read less <
ANR Project
Equations hyperboliques dans des espaces-temps de la relativité générale : diffusion et résonances. - ANR-05-JCJC-0087
Origin
Hal imported