In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternat...

We consider the Navier-Stokes equations in exterior domains and in the weighted L space. For this purpose, we consider the L − L estimates of Stokes semigroup with weight 〈x〉 type. Our proof is based on the cut-off technique with local energy decay estimate proved by Dan, Kobayashi and Shibata [1] and the weighted L − L estimates of Stokes semigroup in the whole space proved by Kobayashi and Ku...

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as a perturbed vector diffusion equation, instead of as a perturbed Stokes system. To illustrate the advantages of this view, we provide a simple pro...

Controllability properties for the Navier–Stokes system are closely related to observability properties for the adjoint Oseen–Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, a new boundary ...

For two-dimensional periodic Kelvin-filtered Navier–Stokes systems, both positively and negatively invariant sets Mn, consisting of initial data for which solutions exist for all negative times and exhibiting a certain asymptotic behaviour backwards in time, are investigated. They are proven to be rich in the sense that they project orthogonally onto the sets of lower modes corresponding to the...

We prove Li–Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier–Stokes equations.

The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...

in the present study, the nonlinear model of non-newtonian blood flow in cosine-shape stenosed elastic artery is numerically examined. the model is carried out for axisymmetric, two-dimensional and fully developed blood flow. the vessel wall is assumed to be have time-dependent radius that is important factor for study of blood flow. the cosine-shape stenosis convert to rigid artery by using a ...

The basic concepts and equations of Newtonian Cosmology are presented in the form necessary for the derivation and analysis of the averaged Navier-Stokes-Poisson equations. A particular attention is paid to the physical and cosmological hypotheses about the structure of Newtonian universes. The system of the Navier-StokesPoisson equations governing the cosmological dynamics of Newtonian univers...

We prove the global well-posedness and regularity of the (isotropic) Lagrangian averaged Navier{Stokes (LANS-¬ ) equations on a three-dimensional bounded domain with a smooth boundary with no-slip boundary conditions for initial data in the set fu 2 Hs \H1 0 j Au = 0 on @« ; div u = 0g, s 2 [3; 5), where A is the Stokes operator. As with the Navier{Stokes equations, one has parabolic-type regul...