A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational inequality, prove an existence and uniqueness result, present an error estimate, and discuss a numerical realization using an iterative Uzawa-type method. Se...

The mechanical response of soft tissue is commonly characterized from unconfined uniaxial compression experiments on cylindrical samples. However, friction between the sample and the compression platens is inevitable and hard to quantify. One alternative is to adhere the sample to the platens, which leads to a known no-slip boundary condition, but the resulting nonuniform state of stress in the...

The generation of internal gravity waves by oscillating bodies, a classical topic from the late 1960s and early 1970s, has been revived about a decade ago in connection with the generation of the internal tide by the oscillation of the barotropic tide over deep-ocean topography, an important topic for ocean mixing and the energy balance of the Earth–Moon system [1–3]. Most investigations of the...

We derive the equation for the vorticity of the incompressible Oseen problem in a half plane with homogeneous (no slip) boundary conditions. The resulting equation is a scalar Oseen equation with certain Dirichlet boundary conditions which are determined by the incompressibility condition and the boundary conditions of the original problem. We prove existence and uniqueness of solutions for thi...

As the number of applications of micro electro mechanical systems, or MEMS, increase, the variety of flow geometries that must be analyzed at the micro-scale is also increasing. To date, most of the work on MEMS scale fluid mechanics has focused on internal flow geometries, such as microchannels. As applications such as micro-scale flyers are considered, it is becoming necessary to consider ext...

An azimuthally symmetric radially sheared azimuthal flow is driven by a nondiffusive, or residual, turbulent stress localized to a narrow annular region at the boundary of a cylindrical magnetized helicon plasma device. A no-slip condition, imposed by ion-neutral flow damping outside the annular region, combined with a diffusive stress arising from turbulent and collisional viscous damping in t...

In order to predict the variations of the channel ionic resistance with time, we follow the framework proposed by Taylor and Aris to analyze our results. We consider here a channel of radius R, length L, and the diffusion coefficient of the salt in the solution is D. Solving the Navier-Stokes equation for a cylindrical channel, under the assumption of no-slip boundary condition, the velocity pr...

We consider the system of Navier-Stokes equations as a model of the motion of compressible, viscous, “pressureless” fluids in the domain Ω = R+ with the no-slip boundary condition. We construct a global in time regular weak solution, provided that the initial density, ρ0, is bounded and the magnitude of the initial velocity u0 is suitably restricted in the semi-norm ‖ √ ρ0(·)u0(·)‖L2(Ω) + ‖∇u0(...