We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by Rogers--Villaroya, of which we prove a sharper version. As a sample application, we use these results to prove the local well-posedness and the global well-posedness for small initial data of semilinear wave equations in R^3 with quintic or higher monomial nonlinearities.
Posted with permission. Version of record appears here: M. Beceanu and M. Goldberg, "A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions," arXiv:1212.0568v2 [math.AP] Dec. 2012