An elementary proof of Strauss conjecture

Abstract

In this paper, we consider the Cauchy problem for semilinear wave equation in high dimensions. First we use a Morawetz energy estimate which is obtained by integrating on the light cone to get a weighted L2−L2 estimate of the solution, and then give an elementary proof of the weighted Strichartz estimate in Georgiev et al. [3], hence the Strauss conjecture. We also obtain a variant of the weighted Strichartz estimates and give the sharp estimate of the lifespan for the semilinear wave equation with subcritical nonlinearity.