Regularity criterion via the pressure on weak solutions to the 3D Navier-Stokes equations

Qionglei, Chen; Zhifei, Zhang

doi:10.1090/S0002-9939-06-08663-1

Regularity criterion via the pressure on weak solutions to the 3D Navier-Stokes equations
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by Chen Qionglei and Zhang Zhifei PDF

Proc. Amer. Math. Soc. 135 (2007), 1829-1837 Request permission

Abstract:

We consider the regularity of weak solutions to the Navier-Stokes equations in $\mathbb {R}^3$. Let $u$ be a Leray-Hopf weak solution. It is proved that $u$ becomes a regular solution if the pressure $p \in L^1(0,T; \dot B^0_{\infty ,\infty })$.

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