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Uniqueness of weak solutions for fractional Navier-Stokes equations

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Abstract

We prove that if u is a weak solution of the d dimensional fractional Navier-Stokes equations for some initial data u 0, and if u belongs to path space P = L q(0, T;B r p,∞ ) or P = L 1(0, T;B 1∞∞ ), then u is unique in the class of weak solutions whenα > 1. The main tools are Bony decomposition and Fourier localization technique. The results generalize and improve many recent known results.

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Authors and Affiliations

  1. Laboratory of Mathematics and Complex Systems (BNU), Ministry of Education, China, Beijing, 100875, China

    Yong Ding

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yong Ding & Xiaochun Sun

  3. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

    Xiaochun Sun

Authors
  1. Yong Ding
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  2. Xiaochun Sun
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Correspondence to Xiaochun Sun.

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Ding, Y., Sun, X. Uniqueness of weak solutions for fractional Navier-Stokes equations. Front. Math. China 10, 33–51 (2015). https://doi.org/10.1007/s11464-014-0370-x

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  • DOI: https://doi.org/10.1007/s11464-014-0370-x

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