Local Smoothing with a Prescribed Loss for the Schrödinger Equation

DOI10.1007/978-3-0348-0466-0_1zbMath1264.58012arXiv1103.3908OpenAlexW76845825MaRDI QIDQ4912941

Jared Wunsch, Hans Christianson

Publication date: 2 April 2013

Published in: American Journal of Mathematics, Microlocal Methods in Mathematical Physics and Global Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3908

zbMATH Keywords

estimateslocal smoothinglinear Schrödinger equation with a prescribed loss

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Elliptic equations on manifolds, general theory (58J05) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Propagation of singularities; initial value problems on manifolds (58J47) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Smoothness of the fundamental solution of Schrödinger equations with mild trapping ⋮ Near sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping ⋮ The Strauss Conjecture on Asymptotically Flat Space-Times ⋮ Exponential lower resolvent bounds far away from trapped sets ⋮ Propagation through trapped sets and semiclassical resolvent estimates ⋮ Decay of local energy for solutions of the free Schrödinger equation in exterior domains ⋮ High-frequency resolvent estimates on asymptotically Euclidean warped products ⋮ Sharp resolvent bounds and resonance-free regions ⋮ Local smoothing for the Schrödinger equation on a multi-warped product manifold with inflection-transmission trapping ⋮ Quantum Monodromy and nonconcentration near a closed semi-hyperbolic orbit ⋮ Unique continuation for quasimodes on surfaces of revolution: rotationally invariant neighbourhoods ⋮ From resolvent estimates to damped waves ⋮ High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis ⋮ On the interaction of metric trapping and a boundary

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