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Morawetz estimates for the wave equation at low frequency
- Publication Year :
- 2010
-
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.<br />Comment: New version of Theorem 1.1 added that includes refined $\ell^1$-$\ell^\infty$ estimate in dyadic shells. Some changes to exposition
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1011.0906
- Document Type :
- Working Paper