208 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
An Analysis of the Evolution Equations for a Generalized Bioconvective Flow
We prove results on existence and uniqueness of solutions of a system of
equations modeling the evolution of a generalized bioconvective flow. The
mathematical model considered in the present work describes the convective
motion generated by the upward swimming of a culture of microorganisms under
the influence of vertical gravitational forces, in an incompressible viscous
fluid whose viscosity may depend on the concentration of microorganisms
Optimal control problem for the generalized bioconvective flow
In this work, we consider an optimal control problem for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganisms in a fluid. Firstly, we study the existence and uniqueness of weak solutions for this model, moreover we prove the existence of the optimal control and we establish the minimum principle by using Dubovitskii-Milyutin’s formalism.DGI-MEC BFM2003- 06446CGCI MECD-DGU Brazil/Spain 117/06FONDECYT 103094
On an iterative method for approximate solutions of a generalized Boussinesq model
An iterative method is proposed for nding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature
dependent viscosity and thermal conductivity. Under certain conditions, it is
proved that such approximate solutions converge to a solution of the original
problem; moreover, convergence-rate bounds for the constructed approximate solutions are also obtained
Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations
In this paper we study the magneto-micropolar fluid equations in ,
prove the existence of the strong solution with initial data in for
, and set up its blow-up criterion. The tool we mainly use is
Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda type
blow-up criterion for smooth solution which relies on the
vorticity of velocity only.Comment: 19page
The Initial Value Problem for the Equations of Magnetohydrodynamic Type in Non-Cylindrical Domain
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