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arXiv · 0810.0464

The semilinear wave equation on asymptotically euclidean manifolds

Jean-Francois Bony·Dietrich Hafner
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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.

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Jean-Francois Bony, Dietrich Hafner. 2008-10-02. The semilinear wave equation on asymptotically euclidean manifolds. https://arxiv.org/abs/0810.0464

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