On sharp Strichartz estimate for hyperbolic Schrödinger equation on ${\mathbb{T}}^3$

Abstract

We prove the sharp Strichartz estimate for hyperbolic Schrödinger equation on ${\mathbb{T}}^3$ via an incidence geometry approach. As application, we obtain optimal local well-posedness of nonlinear hyperbolic Schrödinger equations.

22 pages, 3 figures