Continuum limit of 2D fractional nonlinear Schrödinger equation

Abstract We prove that the solutions to discrete nonlinear Schrödinger equation with non-local algebraically decaying coupling converge strongly in $$L^2({\mathbb {R}}^2)$$ L 2 ( R ) those of continuum fractional equation, as discretization parameter tends zero. The proof relies on sharp dispersive estimates yield Strichartz are uniform parameter. An explicit computation leading term oscillatory integral asymptotics is used show best constants a family blow up non-locality $$\alpha \in (1,2)$$ α ∈ 1 , approaches boundaries.