Continuum limit of 3D fractional nonlinear Schrödinger equation

In this paper, we investigate the continuum limit theory of the fractional nonlinear Schrödinger equation in dimension 3. We show that the solution of discrete fractional nonlinear Schrödinger equation on hZ^3 will converge strongly in L^2 to the solution of fractional nonlinear Schrödinger equation on R^3, when h->0. The key is proving the uniform-in-h Strichartz estimate for discrete fractional nonlinear Schrödinger equation, by using the uniform estimate of oscillatory integral and Newton polyhedron techniques.