Global existence for semilinear wave equations with scaling invariant damping in 3-D

Abstract

Global existence for small data Cauchy problem of semilinear wave equations with scaling invariant damping in 3-D is established in this work, assuming that the data are radial and the constant in front of the damping belongs to [1.5,2). The proof is based on a weighted L2−L2 estimate for inhomogeneous wave equation, which is established by interpolating between energy estimate and a Morawetz type estimate.