Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Homogenization of the Stokes equation with mixed boundary condition in a porous medium

Stochastic Homogenization of Reflected Stochastic Differential Equations

We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-trans...

The no-slip boundary condition: a review

2 History of the no-slip condition 2 2.1 The previous centuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Traditional situations where slip occurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Newtonian liquids: no-sl...

On the Stochastic Burgers Equation with Moving Boundary

This paper studies the stochastic Burgers equation with moving boundaries. The solution is obtained numerically by employing differentiation matrices which are derived from spectral collocation. The stochastic term is considered only to be timedependent. It is argued that the solely time-dependent stochastic term does not create considerable amount of perturbation in the wave profile between th...