Inhomogeneous Strichartz estimates on manifolds with nonpositive curvature and applications

Abstract

We prove lossless inhomogeneous Strichartz estimates for solutions to the Schrödinger equation on compact manifolds with nonpositive curvature over frequency-dependent time intervals of length $\log λ\cdot λ^{-1} $. As applications, we improve upon the Sobolev norm growth bounds for the cubic NLS established by Planchon, Tzvetkov and Visciglia on 3-dimensional compact manifolds when the manifold also has nonpositive curvature and extend the lossless homogeneous Strichartz estimates on logarithmic time intervals established by the first author and Sogge to Schrödinger operators with critically singular potentials.