We prove the global regularity for both of the 3D Navier-Stokes equations and the 3D Euler equations on R for initial data v0 ∈ H (R). 1 Main Result We are concerned on the following Navier-Stokes equations(Euler equations for ν = 0) describing the homogeneous incompressible fluid flows in R. (NS)ν 

We present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in [6], and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equation...

We show existence of measure attractors for 2-D stochas-tic Navier-Stokes equations with general multiplicative noise. Abstract. We show existence of measure attractors for 2-D sto-chastic Navier-Stokes equations with general multiplicative noise. 1. Introduction This paper is concerned with existence of attractors in connection with stochastic Navier-Stokes equations in dimension 2. For determ...

On regularity of stationary Stokes and Navier-Stokes equations near boundary KYUNGKEUN KANG Received: date / Revised version: date – c Springer-Verlag 2001 Abstract. We obtain local estimates of the steady-state Stokes system “without pressure” near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations i...

We prove the global well-posedness and regularity of the (isotropic) Lagrangian averaged Navier{Stokes (LANS-¬ ) equations on a three-dimensional bounded domain with a smooth boundary with no-slip boundary conditions for initial data in the set fu 2 Hs \H1 0 j Au = 0 on @« ; div u = 0g, s 2 [3; 5), where A is the Stokes operator. As with the Navier{Stokes equations, one has parabolic-type regul...

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods a...

The Stokes equations are the linearization of the incompressible Navier-Stokes equations about zero. They may be derived directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. The present paper establishes this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels....

We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in the case when the dissipation degree is sufficiently small.

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the ...

We prove some estimates for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations under assumptions that certain invariant functionals of the velocity field are bounded. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.