2017/03/23 by Jason Metcalfe, Jacob Sterbenz, Metcalfe, Jason +3 · 1 citation
Mathematics · #35B40 #35L05 #35P25 #35R01 #58J45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1703.08064
openalex publication_date 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider local energy decay estimates for solutions to scalar wave\nequations on nontrapping asymptotically flat space-times. Our goals are\ntwo-fold. First we consider the stationary case, where we can provide a full\nspectral characterization of local energy decay bounds; this characterization\nsimplifies in the stationary symmetric case. Then we consider the almost\nstationary, almost symmetric case. There we establish two main results: The\nfirst is a "two point" local energy decay estimate which is valid for a general\nclass of (non-symmetric) almost stationary wave equations which satisfy a\ncertain nonresonance property at zero frequency. The second result, which also\nrequires the almost symmetry condition, is to establish an exponential\ntrichotomy in the energy space via finite dimensional time dependent stable and\nunstable sub-spaces, with an infinite dimensional complement on which solutions\ndisperse via the usual local energy decay estimate.\n