Uniqueness of weak solutions for fractional Navier-Stokes equations

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=L^q(\mathrm{0},T;B_{p,\infty }^r)\mathrm{o}\mathrm{r}p=L^{\mathrm{1}}(\mathrm{0},T;B_{\infty ,\infty }^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

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