We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in R. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstro...

We introduce a construction of regular solutions to the Navier– Stokes equations which is specifically designed for the study of their asymptotic expansions. Using this construction, we give sufficient conditions for the convergence of those expansions. We also construct suitable normed spaces in which they converge. Moreover, in these spaces, the normal form of the Navier–Stokes equations asso...

We discuss the regularity of solutions of 2D incompressible NavierStokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W forcing of the Navier-Stokes equ...

This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. With a particular mesh construction, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein t...

We construct solutions for the Navier-Stokes equations in three dimensions with a time periodic force which is of compact support in a frame that moves at constant speed. These solutions are related to solutions of the problem of a body which moves within an incompressible fluid at constant speed and rotates around an axis which is aligned with the motion. In contrast to other authors who anala...

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (−1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

1. Introduction. Recently A. Chorin has found a numerical scheme for solving the Navier-Stokes equations which has the pleasing feature of not breaking down at high Reynolds numbers R [5]. The purpose of this announcement is to present a formula «2) below) which is designed to establish the convergence of Chorin's time step iteration procedure, assuming that the relevant equations (heat equatio...

In this paper A Geometrical Design Method for Blade’s surface I in the impeller is provided here I is a solution to a coupling system consisting of the well-known Navier-Stokes equations and a four order elliptic boundary value problem . The coupling system is used to describe the relations between solutions of Navier-Stokes equations and the geometry of the domain occupied by fluids, and also ...

We prove uniform existence results for the full Navier-Stokes equations for time intervals which are independent of the Mach number, the Reynolds number and the Péclet number. We consider general equations of state and we give an application for the low Mach number limit combustion problem introduced by Majda in [18].