Remark on uniqueness of mild solutions to the Navier-Stokes equations

We investigate a limiting uniqueness criterion to the Navier-Stokes equations. We prove that the mild solution is unique under the class C([0,T);bmo-1)∩Lloc∞((0,T);L∞), where bmo-1 is the “critical” space including Ln. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo-1.