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arXiv · 2501.10737

Continuum limit of 3D fractional nonlinear Schr\"odinger equation

Jiajun Wang
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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.

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Jiajun Wang. 2025-01-18. Continuum limit of 3D fractional nonlinear Schr\"odinger equation. https://arxiv.org/abs/2501.10737

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