Continuum limit of 3D fractional nonlinear Schr\"odinger 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 hZ3 will converge strongly in L2 to the solution of fractional nonlinear Schr\"odinger equation on R3, 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.
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