Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Local in time regularity properties of the Navier-Stokes equations. (English) Zbl 1175.35100 Indiana Univ. Math. J. 56, No. 5, 2111-2131 (2007). For a weak solution \(u\) of the Navier-Stokes equations in a smooth domain of \({\mathbb R}^3\) in a time interval \([0,T)\) for \(0<T\leq \infty\), with initial value \(u_0\), the authors use new assumptions, beyond classical Serrin’s additional conditions, on \(u_0\) in order to prove various local and global regularity properties of \(u\). Reviewer: Bernard Ducomet (Bruyères le Châtel) Cited in 1 ReviewCited in 13 Documents MSC: 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35B65 Smoothness and regularity of solutions to PDEs Keywords:instationary Navier-Stokes equations; local in time regularity; Serrin’s condition PDF BibTeX XML Cite \textit{R. Farwig} et al., Indiana Univ. Math. J. 56, No. 5, 2111--2131 (2007; Zbl 1175.35100) Full Text: DOI