In this paper we investigate the spatiotemporal dynamics of a diatomic fluid undergoing zero mean oscillatory flow in a slit pore. The study is based on nonequilibrium molecular dynamics simulations together with two limiting solutions to the Navier-Stokes equations which include the effect of molecular rotation. By examining the viscoelastic properties of the system we can estimate the extent ...

In recent years there has been lots of interest in the use of first-order system leastsquares method (FOSLS) for numerical approximations of elliptic partial differential equations, Stokes equations, elasticity and Navier-Stokes equations. In this paper we will provide a brief review of FOSLS around elliptic problems and Stokes equations. FOSLS is to find a minimization solution which minimizes...

We prove Li–Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier–Stokes equations.

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to...

In a 1997 paper, Ball defined a generalised semiflow as a means to consider the solutions of equations without (or not known to possess) the property of uniqueness. In particular he used this to show that the 3d Navier-Stokes equations have a global attractor provided that all weak solutions are continuous from (0,∞) into L2. In this paper we adapt his framework to treat stochastic equations: w...

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity, η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. As same as the 3D Navier-Stokes equations, the regularity of ...

Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. Stress (tension) tensors are considered, obtained by the use of the method of Lagrangians with covariant derivatives (MLCD). On the basis of the covariant Noether's identities for the energy-momentum tensors, Navier-Stokes' identities are found and generalized Navier-Cauchy as well as Navi...

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...