Smoothing effect for time-degenerate Schr\"odinger operators
Analysis of PDEs
2022-01-20 v1
Abstract
In this work we consider an example of a linear time-degenerate Schr\"odinger operator. We show that with the appropriate assumptions the operator satisfies a Kato smoothing effect. We also show that the solutions to the nonlinear initial value problems involving this operator and polynomial derivative nonlinearities are locally well-posed and their solutions also satisfy the same smoothing estimates as the linear solutions.
Cite
@article{arxiv.2001.06708,
title = {Smoothing effect for time-degenerate Schr\"odinger operators},
author = {Serena Federico and Gigliola Staffilani},
journal= {arXiv preprint arXiv:2001.06708},
year = {2022}
}