Strichartz estimates for the wave equation on a 2d model convex domain
arXiv:2008.03598 · doi:10.1016/j.jde.2021.08.011
Abstract
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix we obtain, despite their number increasing like the inverse square root of the distance from the source to the boundary. As a consequence, we improve known Strichartz estimates for the wave equation. Several improvements on our previous parametrix construction are obtained along the way and are of independent interest for further applications.
arXiv commentfinal version
References in corpus (4)
- Strichartz estimates for the wave equation on manifolds with boundary
- Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case
- New counterexamples to Strichartz estimates for the wave equation on a 2d model convex domain
- Dispersive estimates for the wave and the Klein-Gordon equations in large time inside the Friedlander domain