Endpoint Strichartz estimate for the damped wave equation and its application

Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to the unconditional uniqueness for the energy critical nonlinear damped wave equation. This problem seems not to be solvable as the perturbation of the wave equation.