to perhaps the fact that the turbulence model equations are solved only to obtain the eddy viscosity and also the Many researchers use a time-lagged or loosely coupled approach in solving the Navier–Stokes equations and two-equation turbuconvenience of simply adding separate routines to an exlence model equations in a time-marching method. The Navier– isting Navier–Stokes code. Consequently, ma...

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...

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 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 ...

 Abstract : The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L2-...

The aim of this lecture is to give an overview on modern numerical methods for the computation of incompressible flows. We start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes ...

In this paper we prove the logarithmically improved Beale-Kato-Majda's criterion to the three-dimensional incompressible Euler and Navier-Stokes equations as well as the logarithmically improved Serrin's criteria to the three-dimensional incompressible Navier-Stokes equations.

in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of timedependent NavierStokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system c...