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arXiv · 1103.0521

The Schroedinger Equation with Potential in Rough Motion

Marius Beceanu·Avy Soffer
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Abstract

This paper proves endpoint Strichartz estimates for the linear Schroedinger equation in $R^3$, with a time-dependent potential that keeps a constant profile and is subject to a rough motion, which need not be differentiable and may be large in norm. The potential is also subjected to a time-dependent rescaling, with a non-differentiable dilation parameter. We use the Strichartz estimates to prove the non-dispersion of bound states, when the path is small in norm, as well as boundedness of energy. We also include a sample nonlinear application of the linear results.

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Marius Beceanu, Avy Soffer. 2011-03-02. The Schroedinger Equation with Potential in Rough Motion. https://arxiv.org/abs/1103.0521

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