Navier-Stokes equation. The expression is the nonlinear part of the equation and features in the approximation of the flow’s Reynold’s number (see Remarks 5.2(3), on page 721 of [2]). In other words, we discretize the linearized , non-homogeneous Navier-Stokes problem, representing the 3-D slow flow of a fluid. A typical example of a slow Navier-Stokes fluid flow is ground water through an aqui...

This paper is devoted to the study of a stationary problem consisting of the Boussinesq approximation of the Navier–Stokes equations and two convection–diffusion equations for the temperature and concentration, respectively. The equations are considered in 3D and a velocity–pressure formulation of the Navier–Stokes equations is used. The problem is complicated by nonstandard boundary conditions...

We study the local exponential stabilization, near a given steady-state flow, of solutions of the Navier-Stokes equations in a bounded domain. The control is performed through a Dirichlet boundary condition. We apply a linear feedback controller, provided by a well-posed infinite dimensional Riccati equation. We give a characterization of the domain of the closed-loop operator which is obtained...

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0 < t 6 T in some bounded three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and tha...

In this paper we study a class of quasi-variational-hemivariational inequalities in reflexive Banach spaces. The contain convex potential, locally Lipschitz superpotential, and implicit obstacle set constraints. Solution existence compactness the solution to inequality problem are established based on Kakutani–Ky Fan fixed point theorem. applicability results is illustrated by steady-state Osee...

We obtain error estimates for the numerical approximation of a distributed control problem governed by the stationary Navier–Stokes equations, with pointwise control constraints. We show that the L2-norm of the error for the control is of order h2 if the control set is not discretized, while it is of order h if it is discretized by piecewise constant functions. These error estimates are obtaine...

In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes– Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing proper...

The Navier-Stokes equations are solved exactly, assuming the Navier slip boundary condition, for flow between coaxial circular cylinders (with possibly different slip lengths at the inner and outer walls), and flow in an equilateral triangular pipe. The velocity fields and total flow rates are found analytically. A relatively small slip length can lead to a large increase in the total rate of f...

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

We consider the two-dimensional time-harmonic elastic wave scattering problem for an unbounded rough surface, due to an inhomogeneous source term whose support lies within a finite distance above the surface. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the elastic displacement vanishes. We propose an upward propagating radiati...