Weighted Strichartz estimates and existence of self-similar solutions for semilinear wave equations

Abstract

We study the existence of self-similar solutions to the Cauchy problem for semilinear wave equations with power type nonlinearity. Radially symmetric self-similar solutions are obtained in odd space dimensions when the power is greater than the critical one that are widely referred to in other existence problems of global solutions to nonlinear wave equations with small data. This result is a partial generalization of [11] to odd space dimensions. To construct self-similar solutions, we prove the weighted Strichartz estimates in terms of weak Lebesgue spaces over space-time.