Probabilistic Radial Strichartz Estimates and Its Application

Abstract

In this paper, we consider the Cauchy problem for the linear dispersive equations. We establish the probabilistic radial Strichartz estimates for a randomization preserving the radial symmetry. As an application, we prove almost sure local well-posedness along with small data global existence and scattering for the radial mass-critical fractional Schrödinger equation.