On regularity criteria in terms of pressure for the Navier-Stokes equations in \(\mathbb{R} ^3\). (English) Zbl 1075.35044

Zhou, Yong

Proc. Am. Math. Soc. 134, No. 1, 149-156 (2006).

Summary: 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 L. C. Berselli and G. P. Galdi [Proc. Am. Math. Soc. 130, No. 12, 3585–3595 (2002; Zbl 1075.35031)].

MSC:

35Q30	Navier-Stokes equations
35B65	Smoothness and regularity of solutions to PDEs
35B45	A priori estimates in context of PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

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

Citations:

Zbl 1075.35031

References:

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