A sharp Strichartz estimate for the wave equation with data in the energy space

TL;DR

This paper establishes a precise bilinear estimate for the wave equation, determining the optimal constant in the Strichartz inequality that bounds the solution's spacetime norm using energy data, and identifies the maximisers.

Contribution

It provides the first sharp bilinear estimate for the wave equation in the energy space and characterizes the extremisers for the Strichartz inequality.

Findings

Sharp bilinear estimate for the wave equation

Exact constant in the Strichartz inequality

Characterization of maximisers

Abstract

We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the $L^4_{t,x}(\R^{5+1})$ norm of the solution in terms of the energy. We also characterise the maximisers.