Strichartz estimates for the wave equation on manifolds with boundary

TL;DR

This paper establishes new Strichartz estimates for the wave equation on manifolds with boundary, enabling the authors to prove global existence and scattering results for critical and subcritical wave equations in low dimensions.

Contribution

The paper introduces novel mixed-norm Strichartz estimates on manifolds with boundary, leading to new well-posedness and scattering results for wave equations with boundary conditions.

Findings

Global existence for subcritical wave equations in 4D

Global existence for critical wave equations with small data

Scattering results for 3D wave equations with boundary conditions

Abstract

We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcricital case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions.