GLOBAL BEHAVIORS OF DEFOCUSING SEMILINEAR WAVE EQUATIONS

In this paper, we investigate the global behaviors of solutions to defocusing semi-linear wave equations in R1+d with d >= 3. We prove that in the energy space the solution verifies the integrated local energy decay estimates for the full range of energy subcritical and critical powers. For the case where p > d+1/d-1, we derive a uniformweighted energy bound for the solution as well as inverse polynomial decay of the energy flux through hypersurfaces away from the light cone. As a consequence, the solution scatters in the energy space and in the critical Sobolev space for p with an improved lower bound. This in particular extends the existing scattering results to higher dimensions without spherical symmetry.