2006/11/09 by Jeremy Marzuola, Marzuola, Jeremy, Jason Metcalfe +3
Mathematics · #35A17 (Secondary) #35S05 (Primary) 35A22 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A17 #msc:35A22 #msc:35S05
paper · pdf · doi:10.48550/arxiv.math/0611252
9 pages, no figures
arxiv created 2010/09/27 · arxiv updated 2010/09/29
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.