J. Dynamics and Diff. Eqns., in press, 2004. The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations....

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy....

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this pap...

This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward selfsimilar solutions with finite total energy, which generalizes the results for the case of the isothermal compressible Navier-Stokes equations in Z. Guo and S. Jiang (Self-similar solutions to ...

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corr...

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has...

We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the or...

This paper studies the quasi-neutral limit of pressureless Navier-Stokes-Poisson equations in plasma physics in the torus T. For well prepared initial data the convergence of solutions of compressible Navier-Stokes-Poisson equations to the solutions of incompressible Navier-Stokes equations is justified rigorously by using the curl-div decomposition of the gradient. And a priori estimates with ...