Continuum limit of 3D fractional nonlinear Schr\"odinger equation
Analysis of PDEs
2025-01-22 v1
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.
Cite
@article{arxiv.2501.10737,
title = {Continuum limit of 3D fractional nonlinear Schr\"odinger equation},
author = {Jiajun Wang},
journal= {arXiv preprint arXiv:2501.10737},
year = {2025}
}
Comments
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