Abstract: In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain Ω ⊂ R, d = 2, 3. We prove that for a vortex patch initial data the weak Leray solutions of the incompressible Navier-Stokes equations with Navier boundary conditions will converge (locally in time for d = 3 and globally in time for d = 2) to a vo...

A relativistic Navier-Stokes equation is constructed as the equation of motion of a gauge-invariant bosonic lagrangian. It is shown that the quantum-electrodynamic-like lagrangian is suitable for this purpose with a particular form of gauge field, A µ = φ, A ≡ −c 2 1 − | v| 2 /c 2 , − v. The equation of motion coincides with the classical Navier-Stokes equation at non-relativistic limit | v| ≪ c.

With the advent of microscale and nanoscale devices, the Navier-slip boundary condition as a macroscale model of fluid behaviour at a solid wall has seen renewed interest. The penalty concept and variational formulation are extended here to treat partial slip and related boundary conditions in viscous flow simulation. An analysis of the penalty partial-slip formulation permits us to relate it t...

We present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in [6], and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equation...

In [1], T. Clopeau, A. Mikelić, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit satisfies the incompressible Euler equations and their result ultimately includes flows generated by bounded initial vorticities. Our purpose in this article is to ad...

In this paper, we study the 3D axisymmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some Lp norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction bet...

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they relate to LES (ii) to introduce...

This paper gives an example of a periodic, smooth, divergencefree initial vector field and a periodic and bounded external force such that there exist a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions but the solution cannot be continued to the whole space. The example also shows that the solutions to the Navier-Stokes equation...

The applicability of three numerical approximation methods of solving the Navier-Stokes equations (local stagnation streamline approximation, ‘parabolized’ equations, and the thin-viscous-shock-layer approach) have been analyzed to study nonequilibrium hypersonic viscous flows near blunt bodies. These approximations allow reducing the calculation time by factor of 10 in comparison with the time...

In a recent paper [11], Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν. keywords. navier-Stokes equations; Incom...