Unconditional uniqueness of solution for H˙sc critical NLS in high dimensions

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of H˙sc (0≤sc<10≤sc<1) critical nonlinear Schrödinger equations (NLS). By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in Ct(I;H˙sc(Rd)) for d≥6d≥6. This extends earlier results by Yin Yin Su Win and Y. Tsutsumi [19] and Cazenave [3].