Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation

Details Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation

2007-06-28

arxiv.org/abs/0706.4315v2

Mathematics

Analysis of PDEs

8 pages, 1 figure

Scientific paper

This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schr\"odinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schr\"odinger equation.

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