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arXiv · 1606.00959

Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space

Junyong Zhang·Jiqiang Zheng
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Abstract

We study the nonlinear Klein-Gordon equation on a product space $M=\R\times X$ with metric $\tilde{g}=dt^2-g$ where $g$ is the scattering metic on $X$. We establish the global-in-time Strichartz estimate for Klein-Gordon equation without loss of derivative by using the microlocalized spectral measure of Laplacian on scattering manifold showed in \cite{HZ} and a Littlewood-Paley squarefunction estimate proved in \cite{Zhang}. We prove the global existence and scattering for a family of nonlinear Klein-Gordon equations for small initial data with minimum regularity on this setting.

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Junyong Zhang, Jiqiang Zheng. 2016-06-03. Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space. https://doi.org/10.1007/s12220-018-00100-3

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