Wave packet parametrices for evolutions governed by PDO's with rough symbols

Details Wave packet parametrices for evolutions governed by PDO's with rough symbols Wave packet parametrices for evolutions governed by PDO's with rough symbols

2006-11-09

arxiv.org/abs/math/0611252v2

Mathematics

Analysis of PDEs

9 pages, no figures

Scientific paper

In this note, we consider wave packet parametrices for Schrodinger-like evolution equations. Under an integrability condition along the flow, we prove that the flow is then globally well-defined and bilipschitz. Under an additional smallness assumption, we prove that the kernel of the phase space operator decays rapidly away from the graph of the Hamilton flow. This can be used to prove that smoothness is preserved for finite times by the flow of the equation.

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