## Differential and Integral Equations

### Bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary and cubic NLS

Jin-Cheng Jiang

#### Abstract

In this paper, we establish bilinear and gradient bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary. Using these estimates, we can infer the local well-posedness of the cubic nonlinear Schrödinger equation in $H^s$ for every $s>\frac{2}{3}$ on such manifolds.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 1/2 (2011), 83-108.

Dates
First available in Project Euclid: 20 December 2012