We show that in a tubular domain with sufficiently small width, the normal and tangential gradients of a harmonic function have almost the same L norm. This estimate yields a sharp estimate of the pressure in terms of the viscosity term in the Navier-Stokes equation with no-slip boundary condition. By consequence, one can analyze the NavierStokes equations simply as a perturbed vector diffusion...

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

We prove instability of a part of a branch of viscous incompressible fluid flows induced by a shrinking sheet. These flows are exact solutions of the Navier-Stokes equation.

We use the bivariate spline method to solve the time evolution Navier-Stokes equations numerically. The bivariate spline we use in this paper is the spline space of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the Navier-Stokes equations is employed. Galerkin's method is applied to discretize the space variables of the nonlinear fourth order...

We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier–Stokes equations for the two-phase flow in the bulk, which are coupled to the transport equation for the insoluble surfactant on the interface that separates the two phases. We combine the evolving surface finite element method with an approach prev...

The fluid dynamics of expanding and contracting tube is investigated mathematically using both the Navier-Stokes and continuity equations for an incompressible viscous fluid. The problem admits similarity solution, thereby reducing the unsteady Navier-Stokes equations to a parameter dependent fourth order nonlinear ordinary differential equation. Analytical solutions are constructed for the pro...

Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental a...

In the following paper we will consider Navier-Stokes problem and it's interpretation by hyperbolic waves, focusing on wave propagation. We will begin with solution for linear waves, then present problem for non-linear waves. Later we will derive for numerical solution using PDE's. Also we will design a Matlab program to solve and simulate wave propagation. Keywords1: Navier-Stokes equations, F...

The concept of entropy conservation, stability, and consistency is applied to systems of hyperbolic equations to create new flux functions for the scalar and systems of conservation laws. Firstty, Burgers' equation is modelled, followed by the Navier-Stokes equations. The new models are compared with the pre-existing entropy consistent fluxes at selected viscosity levels; it is found that the s...

In this paper, analytical and numerical methods for simulating squeeze-film air damping affecting suspended and perforated movable micro-surfaces are analyzed. Numerical solutions are obtained by full 3-D Navier-Stokes numerical analysis, carried out by a commercial finite element code, COMSOL Multiphysics, and are compared with those obtained using different analytical models proposed in liter...