We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Kolmogorov equation approach.

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1])

We consider dynamics system with damping, which are obtained by some transformations from the system of incompressible Navier-Stokes equations. These have similar properties to original Navier-Stokes equations the scaling invariance. Due to the presence of the damping term, conclusions are different with proving the origin of the incompressible Navier-Stokes equations and get some new conclusio...

The equations of motion of conducting fluid in a magnetic field are formulated. These consist of three sets. First is the mass conservation equation, second Navier Stokes equation which is Newton’s second law taking into account the force of magnetic field on moving charges. The electrical field effects are neglected as is usually done in MHD. The third set is Maxwell’s equation especially to m...

sediment flushing of reservoirs is an operational technique, whereby previously accumulated sediments in the reservoirs are hydraulically removed by accelerated flow when the bottom desiltingoutlets of the dam are opened. in this research, the process of sediment flushing is simulated by a three dimensional numerical model in which sediment and flow interaction are reflected in the reservoirs. ...

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as a perturbed vector diffusion equation, instead of as a perturbed Stokes system. To illustrate the advantages of this view, we provide a simple pro...

In this paper, we consider a model equation for the Navier--Stokes strain equation. This has same identity enstrophy growth and number of regularity criteria as full Navier-Stokes equation, is also an evolution on constraint space. We prove finite-time blowup which shows that space are not sufficient their own to guarantee global Navier-Stokes. The mechanism self-amplification strain, consisten...

A finite difference lattice Boltzmann method based on the Bhatnagar–Gross–Krook-type modeled Boltzmann equation is proposed. Themethod relies on a different lattice equilibriumparticle distribution function and the use of a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as con...

Solutions of the Cauchy problem for the Navier-Stokes equation, in a certain generalized sense, are not unique.

We report on recent progress towards the development of a 3D optimization capability for transonic ow at high Reynolds numbers. In this paper we demonstrate optimization based on the 3D laminar Navier-Stokes equation, and we present validation of the ow analysis scheme based on the 2D Navier-Stokes equations with turbulence modelling.