Global well-posedness for a L2-critical nonlinear higher-order Schrödinger equation

We prove the global well-posedness for a L2-critical defocusing cubic higher-order Schrödinger equation, namelyi∂tu+Λku=−|u|2u, where Λ=−Δ and k≥3, k∈Z in Rk with initial data u0∈Hγ, γ>γ(k):=k(4k−1)14k−3.