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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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M. Beceanu and A. Soffer, "The Schroedinger Equation with Potential in Rough Motion," arXiv:1103.0521v1 [math.AP] Mar. 2011

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