Inhomogeneous Strichartz estimates in some critical cases
Classical Analysis and ODEs
2019-02-05 v1 Analysis of PDEs
Abstract
Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a weak-type norm in the temporal variable. We achieve this by establishing such weak-type inhomogeneous Strichartz estimates in an abstract setting. The application to the wave equation rests on a slightly stronger form of the standard dispersive estimate in terms of certain Besov spaces.
Cite
@article{arxiv.1902.01125,
title = {Inhomogeneous Strichartz estimates in some critical cases},
author = {Neal Bez and Jayson Cunanan and Sanghyuk Lee},
journal= {arXiv preprint arXiv:1902.01125},
year = {2019}
}