Neustupa, Jiří; Penel, Patrick Estimates up to the boundary of a weak solution to the Navier-Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor. (English) Zbl 1101.35353 Mucha, Piotr (ed.) et al., Regularity and other aspects of the Navier-Stokes equations. Based on the conference on regularity and other qualitative aspects of the Navier-Stokes equations, Bȩdlewo, Poland, August 31–September 6, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 70, 185-197 (2005). Summary: We formulate sufficient conditions for regularity up to the boundary of a weak solution \(v\) in a subdomain \(\Omega\times (t_1,t_2)\) of the time-space cylinder \(\Omega\times(0,T)\) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that \(\Omega\) is a cube.For the entire collection see [Zbl 1081.35003]. Cited in 2 Documents MSC: 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:regularity up to the boundary; eigenvalues of the rate of deformation tensor PDFBibTeX XMLCite \textit{J. Neustupa} and \textit{P. Penel}, Banach Cent. Publ. 70, 185--197 (2005; Zbl 1101.35353)