Nečas, Jindřich; Neustupa, Jiří New conditions for local regularity of a suitable weak solution to the Navier-Stokes equation. (English) Zbl 1010.35081 J. Math. Fluid Mech. 4, No. 3, 237-256 (2002). Summary: We formulate conditions which guarantee that a suitable weak solution \((v,p)\) to the Navier-Stokes equation (in the sense of L. Caffarelli, R. Kohn and L. Nirenberg [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)]) cannot have a singularity at the point \((x_0,t_0)\in \mathbb{R}^3\times (0,T)\). The usual Prodi-Serrin condition on the velocity \(v\) is substantially replaced by an analogous condition imposed on the negative part \(p_-\) of the pressure \(p\). Cited in 1 ReviewCited in 5 Documents MSC: 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 35B65 Smoothness and regularity of solutions to PDEs Keywords:conditions for local regularity; suitable weak solution; Navier-Stokes equation; Prodi-Serrin condition PDF BibTeX XML Cite \textit{J. Nečas} and \textit{J. Neustupa}, J. Math. Fluid Mech. 4, No. 3, 237--256 (2002; Zbl 1010.35081) Full Text: DOI