The Schroedinger Equation with Potential in Rough Motion

Authors

Marius Beceanu, University at Albany, State University of New YorkFollow
Avy Soffer, Rutgers University - New Brunswick/Piscataway

Document Type

Article

Publication Date

3-2011

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.

Comments

Posted with permission. Version of record appears here:

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

Recommended Citation

Beceanu, Marius and Soffer, Avy, "The Schroedinger Equation with Potential in Rough Motion" (2011). Mathematics and Statistics Faculty Scholarship. 19.
https://scholarsarchive.library.albany.edu/math_fac_scholar/19