We examine a generalised Navier-Stokes theory applicable to fluids composed of non-spherical molecules. We compare the theoretical predictions for flow velocity and viscosity with results obtained from nonequilibrium molecular dynamics (NEMD) simulations of a fluid undergoing gravity fed flow down a rectangular channel. We study two different fluids: one composed of spherical particles and the ...

This article surveys some recent applications of ideas from dynamical systems theory to understand the qualitative behavior of solutions of dissipative partial differential equations with a particular emphasis on the two-dimensional Navier-Stokes equations.

2 Preliminaries in Mathematics and Physics 47 2.1 Surface Theory Based on Moving Frame . . . . . . . . . . . . . . 47 2.1.1. Moving Frame Method . . . . . . . . . . . . . . . . . . . 47 2.1.2. Stokes’ Theorem and Related Identities . . . . . . . . . . 49 2.2 Helfrich’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3 Variational Method Based on Moving Frame . . . . . . . . . . ....

With methods of potential theory we develop a representation of the solution of a coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H−1/2.

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Following Stokes, several authors have studied waves with 120-degree angles at their crests caused on a free surface of fluid by the gravity force. Mathematical analysis, however, shown that similar Stokes waves can be caused by centrifugal force on surfaces where the pressure is constant, and cavitating tip vortex can be examined as a surface of an eventual appearance of axissymmetrical Stokes...

In this paper, we study the solvability of inhomogeneous boundary value problems for the three-dimensional Oseen and Navier–Stokes equations in the following formulation: given function spaces for Dirichlet boundary conditions, initial values, and right-hand side forcing functions, find function spaces for solutions such that the operator generated by the boundary value problem for the Oseen eq...

The effect on the Stokes parameters of a Gaussian Schell model beam on propagation in free space is studied experimentally and results are matched with the theory [X. H. Zhao, et al. Opt. Express 17, 17888 (2009)] that in general the degree of polarization of a Gaussian Schell model beam doesn't change on propagation if the three spectral correlation widths δ xx, δ yy, δ xy are equal and the be...