Abstract and Applied Analysis

On Unique Continuation for Navier-Stokes Equations

Zhiwen Duan, Shuxia Han, and Peipei Sun

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Abstract

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 t0=0 and t1=1 which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.

Article information

Source
Abstr. Appl. Anal., Volume 2015, Special Issue (2014), Article ID 597946, 16 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1429104583

Digital Object Identifier
doi:10.1155/2015/597946

Mathematical Reviews number (MathSciNet)
MR3335432

Zentralblatt MATH identifier
1356.35158

Citation

Duan, Zhiwen; Han, Shuxia; Sun, Peipei. On Unique Continuation for Navier-Stokes Equations. Abstr. Appl. Anal. 2015, Special Issue (2014), Article ID 597946, 16 pages. doi:10.1155/2015/597946. https://projecteuclid.org/euclid.aaa/1429104583


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