We study the driven cavity flow using the Navier slip boundary condition. Our results have shown that the Navier slip boundary condition removes the corner singularity induced by the no-slip boundary condition. In the low Reynolds number case, the behavior of the tangential stress is examined and the results are compared with the analytic results obtained in [14]. For the high Reynolds number, ...

Consider a viscous liquid droplet spreading on a surface. The classical slip condition at the liquid–solid interface is the no–slip condition. However, this condition lead to infinite dissipation of energy for propagating contact lines (“no–slip paradox”). For this reason other slip conditions such as the Navier–slip have been introduced. We prove well–posedness for a reduced 1–d fluid model mo...

Abstract We study the $$L^{\infty }$$ L ∞ stability of Navier-Stokes equations in half-plane with a viscosity-dependent Navier friction boundary condition around shear profiles which are linearly unstable for Euler equation. The dependence from viscosity is given as $$\...

We consider an inverse problem of determining a spatially varying factor in a source term in a nonstationary linearized Navier-Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof based on a new Carleman estimate for the Navier-Stokes ...

In this paper we show the existence of regular solutions of the Rothe–approximation of the unsteady Navier–Stokes equations with periodic boundary condition in arbitrary dimension. The result relies on techniques developed by the authors in the study of the higher–dimensional steady Navier–Stokes equations.

In this paper we consider the three–dimensional Navier–Stokes equations in an infinite channel. We provide a sufficient condition, in terms of ∂zp, where p is the pressure, for the global existence of the strong solutions to the three–dimensional Navier–Stokes equations. AMS Subject Classifications: 35Q35, 65M70