On regularity criteria in terms of pressure for the Navier-Stokes equations in ℝ³

Zhou, Yong

doi:10.1090/S0002-9939-05-08312-7

On regularity criteria in terms of pressure for the Navier-Stokes equations in $\mathbb {R}^3$
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Proc. Amer. Math. Soc. 134 (2006), 149-156 Request permission

Abstract:

In this paper we establish a Serrin-type regularity criterion on the gradient of pressure for the weak solutions to the Navier-Stokes equations in $\mathbb {R}^3$. It is proved that if the gradient of pressure belongs to $L^{\alpha ,\gamma }$ with $2/\alpha +3/\gamma \leq 3$, $1\leq \gamma \leq \infty$, then the weak solution is actually regular. Moreover, we give a much simpler proof of the regularity criterion on the pressure, which was showed recently by Berselli and Galdi (Proc. Amer. Math. Soc. 130 (2002), no. 12, 3585–3595).

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