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arXiv · 2001.06708

Smoothing effect for time-degenerate Schrödinger operators

Serena Federico·Gigliola Staffilani
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Abstract

In this work we consider an example of a linear time-degenerate Schrödinger 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.

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Serena Federico, Gigliola Staffilani. 2020-01-18. Smoothing effect for time-degenerate Schrödinger operators. https://doi.org/10.1016/j.jde.2021.07.006

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