Continuum limit of 3D fractional nonlinear Schrödinger equation

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