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Zbl 1075.35044
Zhou, Yong
On regularity criteria in terms of pressure for the Navier-Stokes equations in $\Bbb{R} ^3$.
(English)
[J] Proc. Am. Math. Soc. 134, No. 1, 149-156 (2006). ISSN 0002-9939; ISSN 1088-6826/e

Summary: We establish a Serrin-type regularity criterion on the gradient of pressure for the weak solutions to the Navier-Stokes equations in $\Bbb{R} ^3$. 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 {\it L. C. Berselli} and {\it G. P. Galdi} [Proc. Am. Math. Soc. 130, No. 12, 3585--3595 (2002; Zbl 1075.35031)].
MSC 2000:
*35Q30 Stokes and Navier-Stokes equations
35B65 Smoothness of solutions of PDE
35B45 A priori estimates
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: regularity criterion; gradient of pressure; weak solutions; Navier-Stokes equations

Citations: Zbl 1075.35031

Cited in: Zbl 1182.35179

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