In this paper we prove a global well-posedness result for tridimensional Navier-Stokes-Boussinesq system with axisymmetric initial data. This system couples Navier-Stokes equations with a transport equation governing the density.

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...

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...

We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [1] and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number...

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...

In this paper, we present first-, second-, and third-order implicit finite-volume schemes for solving the Navier-Stokes equations on unstructured grids based on a hyperbolic formulation of the viscous terms. These schemes are first-, second-, and third-order accurate on irregular grids for both the inviscid and viscous terms and for all Reynolds numbers, not only in the primitive variables but ...

The numerical implementation of a multilevel finite element method for the steadystate Navier–Stokes equations is considered. The multilevel method proposed here for the Navier– Stokes equations is a multiscale method in which the full nonlinear Navier–Stokes equations are only solved on a single coarse grid; subsequent approximations are generated on a succession of refined grids by solving a ...

We study the weak boundary layer phenomenon of the Navier-Stokes equations with generalized Navier friction boundary conditions, u ·n = 0, [S(u)n] tan +Au = 0, in a bounded domain in R when the viscosity, ε > 0, is small. Here, S(u) is the symmetric gradient of the velocity, u, and A is a type (1, 1) tensor on the boundary. When A = αI we obtain Navier boundary conditions, and when A is the sha...