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FIELD Math: CMC
DATE December 07 (Fri), 2018
TIME 16:00-17:30
PLACE 1423
SPEAKER Yang, Changhun
HOST Oh, Sung-Jin
INSTITUTE  
TITLE [Analysis & PDE Learning Seminar] On local smoothing estimates for Schrödinger equations with variable coefficients
ABSTRACT

For the Schrödinger operator, the principal symbol can be considered as a metric and the bicharacteristic flow gives the geodesics on the tangent bundle of the corresponding Riemannian manifold. It is well-known that these types of estimates fail even if we localize in time if there are trapped geodesics.

In this talk, I consider the nontrapping and asymptotically flat symbol and prove the local smoothing estimates. The proof proceeds by the positive commutator method using pseudodifferential operators adapted to the geometry of bicharacteristic flow.

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