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On Unique Continuation for Navier-Stokes Equations

Author

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  • Zhiwen Duan
  • Shuxia Han
  • Peipei Sun

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 and which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.

Suggested Citation

  • Zhiwen Duan & Shuxia Han & Peipei Sun, 2015. "On Unique Continuation for Navier-Stokes Equations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-16, March.
    • Handle: RePEc:hin:jnlaaa:597946
    DOI: 10.1155/2015/597946
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