In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions, i.e., the solutions take form (1.12). The approximate soluti...

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 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 

In this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the threedimensionaFin...

In [14], S. Montgomery-Smith provides a one dimensional model for the three dimensional, incompressible Navier-Stokes equations, for which he proves the blow up of solutions associated to a class of large initial data, while the same global existence results as for the Navier-Stokes equations hold for small data. In this note the model is adapted to the case of two and three space dimensions, w...

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solution...

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.

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...

Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...