A tentative suggestion is made that the flatness of the velocity derivative could reach an infinite value at finite (though very large) Reynolds number, with possible implications for the singularities of the Navier–Stokes equations. A direct test of this suggestion requires measurements at Reynolds numbers presently outside the experimental capacity, so an alternative suggestion that can be te...

We present a block preconditioner for LDG discretizations of Stokes equations. The dependence of its performance on the discretization parameters is investigated. An extension to Oseen equations is shown, yielding efficient and robust solvers in a wide regime of Reynolds numbers.

We give a condition for the periodic, three dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the scale invariant space B ∞,∞, which contains all the known spaces in which there is a global solution for small data. The smallness condition is rather a non...

This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.

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...

For increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier– Stokes equations. The inclusion of higher order terms, such as Burnett, or high-order moment equations, could improve the predictive capabilit...

In this paper, we study the dynamic stability of the 3D axisymmetric NavierStokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An important property of this 1D model is that one can construct from its solutions a family of exact solutions of the 3D Navier-Stokes equations. The nonlinear...

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0 < t 6 T in some bounded three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and tha...

Usually the Stokes equations that govern a flow in a smooth thin domain (with thickness of order ε) are related to the Reynolds equation for the pressure psmooth. In this paper, we show that for a rough thin domain (with rugosities of order ε) the flow is governed by a modified Reynolds equation for a pressure prough. Moreover we find the relation prough = K psmooth where K is an explicit coeff...

Abstract. Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stokes equations on a periodic box. The estimate for the smallest of these inverse scales coincides with the inverse Kolmogorov length, but thereafter the exponents of the Reynolds number rise rapidly for corresp...