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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 597946, 16 pages
Research Article

On Unique Continuation for Navier-Stokes Equations

Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 4 June 2014; Accepted 25 August 2014

Academic Editor: BoQing Dong

Copyright © 2015 Zhiwen Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different times and which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.