Sharp Strichartz estimates for the Schrödinger equation on the sphere

Abstract

In this contribution we investigate the Schrördinger equation associated to the Laplacian on the sphere in the form of sharp Strichartz estimates. We will provided simple proofs for our main theorems using purely the \(L^2\rightarrow L^p\) spectral estimates for the operator norm of the spectral projections (associated to the spherical harmonics) proved in Kwon and Lee (RIMS Kokyuroku Bessatsu 70:33–58, 2018). A sharp index of regularity is established for the initial data in spheres of arbitrary dimension \(d\ge 2\).