Time splitting method for nonlinear Schrödinger equation with rough initial data in L²

We establish convergence results related to the operator splitting scheme on the Cauchy problem for the nonlinear Schrödinger equation with rough initial data in L², {i∂_tu+Δu=λ|u|^pu,(x,t)∈R^d×R₊,u(x,0)=ϕ(x),x∈R^d, where λ∈{−1,1} and p>0. While the Lie approximation Z_L is known to converge to the solution u when the initial datum ϕ is sufficiently smooth, the convergence result for rough initial data is open to question. In this paper, for rough initial data ϕ∈L²(R^d), we prove the L² convergence of the filtered Lie approximation Z_flt to the solution u in the mass-subcritical range, [Formula presented]. Furthermore, we provide a precise convergence result for radial initial data ϕ∈L²(R^d).