129,552 research outputs found
On the approximation of turbulent fluid flows by the Navier-Stokes- equations on bounded domains
The Navier-Stokes- equations belong to the family of LES (Large Eddy
Simulation) models whose fundamental idea is to capture the influence of the
small scales on the large ones without computing all the whole range present in
the flow. The constant is a regime flow parameter that has the
dimension of the smallest scale being resolvable by the model. Hence, when
, one recovers the classical Navier-Stokes equations for a flow of
viscous, incompressible, Newtonian fluids. Furthermore, the
Navier-Stokes- equations can also be interpreted as a regularization of
the Navier-Stokes equations, where stands for the regularization
parameter.
In this paper we first present the Navier-Stokes- equations on
bounded domains with no-slip boundary conditions by means of the Leray
regularization using the Helmholtz operator. Then we study the problem of
relating the behavior of the Galerkin approximations for the
Navier-Stokes- equations to that of the solutions of the Navier-Stokes
equations on bounded domains with no-slip boundary conditions. The Galerkin
method is undertaken by using the eigenfunctions associated with the Stokes
operator. We will derive local- and global-in-time error estimates measured in
terms of the regime parameter and the eigenvalues. In particular, in
order to obtain global-in-time error estimates, we will work with the concept
of stability for solutions of the Navier-Stokes equations in terms of the
norm
Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations
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. Third, a criterion
for the existence of almost periodic (quasi periodic,almost automorphic,
recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes
equations is given. Finally, the authors have derived a global averaging
principle for non-autonomous Navier-Stokes equations.Comment: J. Dynamics and Diff. Eqns., in press, 200
A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion
We establish a Liouville type result for a backward global solution to the
Navier-Stokes equations in the half plane with the no-slip boundary condition.
No assumptions on spatial decay for the vorticity nor the velocity field are
imposed. We study the vorticity equations instead of the original Navier-Stokes
equations. As an application, we extend the geometric regularity criterion for
the Navier-Stokes equations in the three-dimensional half space under the
no-slip boundary condition
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