Partial regularity of solutions to the fractional Navier-Stokes equations

Yukang  Chen; Changhua  Wei

doi:10.3934/dcds.2016033

Article Contents

2016, Volume 36, Issue 10: 5309-5322. Doi: 10.3934/dcds.2016033

This issue Previous Article Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations Next Article Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros

Partial regularity of solutions to the fractional Navier-Stokes equations

Yukang Chen^1, and
Changhua Wei^1,

1.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: September 2015

Revised: December 2015

Published: May 2017

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Abstract

We study the partial regularity of suitable weak solutions to the Navier-Stokes equations with fractional dissipation $\sqrt{-\Delta}^s$ in the critical case of $s=\frac{3}{2}$. We show that the two dimensional Hausdorff measure of space-time singular set of these solutions is zero.

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Mathematics Subject Classification: Primary: 76D03, 76D05; Secondary: 35Q30.

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