Strichartz estimates for partially periodic solutions to Schr\"odinger equations in 4d and applications
Analysis of PDEs
2014-05-05 v1
Abstract
We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to the corresponding linear Schr\"odinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L^4 estimate holds if m=2,3, leaving open the cases m=0,1.
Keywords
Cite
@article{arxiv.1011.0591,
title = {Strichartz estimates for partially periodic solutions to Schr\"odinger equations in 4d and applications},
author = {Sebastian Herr and Daniel Tataru and Nikolay Tzvetkov},
journal= {arXiv preprint arXiv:1011.0591},
year = {2014}
}
Comments
15 pages