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))boolean ANDL(loc)(infinity)((0, T); L-infinity), where bmo(-1) is the critical space including L-n. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo(-1). (C) 2004 Elsevier Inc. All rights reserved.