Local in time regularity properties of the Navier-Stokes equations. (English) Zbl 1175.35100

Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann

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)

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