Guberovic, Rafaela; Schwab, Christoph; Stevenson, Rob Space-time variational saddle point formulations of Stokes and Navier-Stokes equations. (English) Zbl 1295.35354 ESAIM, Math. Model. Numer. Anal. 48, No. 3, 875-894 (2014). The authors investigate simultaneously space-time variational saddle point formulations of the incompressible Stokes and Navier-Stokes equations involving both the velocities and the pressure. They prove that the Stokes operator defined by this variational formulation is boundedly invertible beetween a suitable Hilbert space and the dual of another Hilbert space, thus obtaining well-posedness for the Stokes equations with slip and no-slip boundary conditions. Since the Navier-Stokes operator is Lipschitz continuous under appropriate conditions, the authors are able to use a fixed point argument to prove, for small data, existence for the space-time variational formulation of the Navier-Stokes equations. Reviewer: Gheorghe Moroşanu (Budapest) Cited in 8 Documents MSC: 35Q30 Navier-Stokes equations 76M30 Variational methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D07 Stokes and related (Oseen, etc.) flows Keywords:Stokes; Navier-Stokes; space-time variational saddle-point formulation; well-posedness PDFBibTeX XMLCite \textit{R. Guberovic} et al., ESAIM, Math. Model. Numer. Anal. 48, No. 3, 875--894 (2014; Zbl 1295.35354) Full Text: DOI