Uniqueness of weak solutions for fractional Navier-Stokes equations

doi:10.1007/s11464-014-0370-x

Front. Math. China

2015, Vol. 10

Issue (1) : 33-51 https://doi.org/10.1007/s11464-014-0370-x

RESEARCH ARTICLE

Uniqueness of weak solutions for fractional Navier-Stokes equations

Yong DING^1,²,Xiaochun SUN^2,^3,^*(

)

1. Laboratory of Mathematics and Complex Systems (BNU)Ministry of EducationChinaBeijing 100875China
2. School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China
3. College of Mathematics and StatisticsNorthwest Normal UniversityLanzhou 730070China

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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 u₀and if u belongs to path space p=Lq(0,T;Bp,∞r)or p=L1(0,T;B∞,∞r), then u is unique in the class of weak solutions when α>1. The main tools are Bony decomposition and Fourier localization technique. The results generalize and improve many recent known results.

Keywords Strichartz estimateelliptic Navier-Stokes equationhigher-order elliptic operatorpotential

Corresponding Author(s): Xiaochun SUN

Issue Date: 30 December 2014

Cite this article:

Yong DING,Xiaochun SUN. Uniqueness of weak solutions for fractional Navier-Stokes equations[J]. Front. Math. China, 2015, 10(1): 33-51.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0370-x
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I1/33

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