BONY, Jean Francois; HÄFNER, Dietrich

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BONY, Jean Francois
Institut de Mathématiques de Bordeaux [IMB]

HÄFNER, Dietrich
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

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Comm. Partial Differential Equations. 2010, vol. 35, n° 1, p. 23-67

Resumen en inglés

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.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190977

Proyecto ANR

Equations hyperboliques dans des espaces-temps de la relativité générale : diffusion et résonances. - ANR-05-JCJC-0087

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251