Strichartz estimates on exterior polygonal domains
Abstract
Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-in-time local smoothing estimate in exterior wedge domains with Dirichlet boundary conditions and discuss some nonlinear applications.
Cite
@article{arxiv.1211.1211,
title = {Strichartz estimates on exterior polygonal domains},
author = {Dean Baskin and Jeremy L. Marzuola and Jared Wunsch},
journal= {arXiv preprint arXiv:1211.1211},
year = {2013}
}
Comments
15 pages. This paper has been substantially revised; the results have been improved to include global-in-time estimates in the Dirichlet case. Further revised to include more related scattering references thanks to a careful reading by Fabrice Planchon