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