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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 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.





Author: Jean Francois Bony - Dietrich Häfner -

Source: https://hal.archives-ouvertes.fr/



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