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تسجيل مستخدم جديدLocal Smoothing Estimates near a Trapped Set with Infinitely Many Connected Components
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We prove a local smoothing result for the Schrodinger equation on a class of surfaces of revolution which have infinitely many trapped geodesics. Our main result is a local smoothing estimate with loss (compared to cite{ChMe-lsm}) depending on the accumulation rate of the critical points of the profile curve. The proof uses an h-dependent version of semiclassical propagation of singularities, and a result on gluing an h-dependent number of cutoff resolvent estimates.
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