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arXiv · 1011.0906

Morawetz estimates for the wave equation at low frequency

András Vasy·Jared Wunsch
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Abstract

We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low frequencies, independent of the geometry of the compact part of the manifold. We further prove a new type of Morawetz estimate in this context, with both hypotheses and conclusion localized inside the forward light cone. This result allows us to gain a 1/2 power of $t$ decay relative to what would be dictated by energy estimates, in a small part of spacetime.

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András Vasy, Jared Wunsch. 2010-11-03. Morawetz estimates for the wave equation at low frequency. https://arxiv.org/abs/1011.0906

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