We show time-weighted estimates in Lorentz spaces for the linear wave equation with singular potential. As a consequence, assuming radial symmetry on initial data and potentials, we obtain well-posedness of global solutions in critical weak- spaces for semilinear wave equations. In particular, we can consider the Hardy potential for small . Self-similar solutions are obtained for potentials and initial data with the right homogeneity. Our approach relies on performing estimates in the predual of weak-, i.e., the Lorentz space .
"Time-weighted estimates in Lorentz spaces and self-similarity for wave equations with singular potentials." Anal. PDE 10 (2) 423 - 438, 2017. https://doi.org/10.2140/apde.2017.10.423