Local smoothing for the Schrödinger equation with a prescribed loss
Local smoothing for the Schrödinger equation with a prescribed loss
We consider a family of surfaces of revolution, each with a single periodic geodesic which is degenerately unstable. We prove a local smoothing estimate for solutions to the linear Schrödinger equation with a loss that depends on the degeneracy, and we construct explicit examples to show our estimate is saturated …