Regularity of a suitable weak solution to the Navier-Stokes equations as a consequence of regularity of one velocity component. (English) Zbl 0953.35113

Neustupa, Jiří; Penel, Patrick

Sequeira, Adélia (ed.) et al., Applied nonlinear analysis. In honor of the 70th birthday of Professor Jindřich Nečas. New York, NY: Kluwer Academic/Plenum Publishers. 391-402 (1999).

Summary: We show that if \((v;p)\) is a suitable weak solution to the Navier-Stokes equations (in the sense of L. Caffarelli, R. Kohn and L. Nirenberg) such that \(v_3\) (the third component of \(v)\) is essentially bounded in a sub-domain \(D\) of a time-space cylinder \(Q_T\) then \(v\) has no singular points in \(D\).
For the entire collection see [Zbl 0939.00054].

MSC:

35Q30	Navier-Stokes equations
35D10	Regularity of generalized solutions of PDE (MSC2000)
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids

Keywords:

Navier-Stokes equations; weak solutions; regularity