Global existence without decay for quadratic Klein-Gordon equations

Tobias Schottdorf

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arXiv · 1209.1518

Global existence without decay for quadratic Klein-Gordon equations

Tobias Schottdorf

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Abstract

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering result is proven for small H^s data, s >= max(1/2, (n-2)/2), using the contraction mapping technique in U^2/V^2 based spaces. The result demonstrates that global results and scattering hold in this setting without the need to impose strong decay on the initial data.

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Tobias Schottdorf. 2012-09-19. Global existence without decay for quadratic Klein-Gordon equations. https://arxiv.org/abs/1209.1518

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