Well–posedness for the periodic hyperbolic nonlinear Schrödinger equations

Source abstract

In this paper, we study the Hyperbolic Nonlinear Schrödinger (HNLS) equation on general tori of dimensions [Formula: see text]. In particular, we establish sharp well-posedness results up to the endpoint cases for all odd nonlinearities. For higher dimensions and nonlinearities, we further extend the well-posedness theory to the critical regularity. For this purpose, we prove the scale-invariant Strichartz estimates and multi-linear estimates for hyperbolic Schrödinger equations on general tori.