A computational procedure based on a divergence-free H(div) method is presented for the Stokes and Navier-Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding H(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the calculation....

In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternat...

We consider the Navier-Stokes equations in exterior domains and in the weighted L space. For this purpose, we consider the L − L estimates of Stokes semigroup with weight 〈x〉 type. Our proof is based on the cut-off technique with local energy decay estimate proved by Dan, Kobayashi and Shibata [1] and the weighted L − L estimates of Stokes semigroup in the whole space proved by Kobayashi and Ku...

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as a perturbed vector diffusion equation, instead of as a perturbed Stokes system. To illustrate the advantages of this view, we provide a simple pro...

Anti-Stokes/Stokes asymmetries under surface enhanced Raman scattering (SERS) conditions are studied for a wide variety of SERS-active media and different analytes. Evidence is provided for the existence of underlying resonances that create these asymmetries. We show here that these resonances are associated with the electromagnetic coupling between the analyte (probe) and the metal. The work d...

J. Dynamics and Diff. Eqns., in press, 2004. 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....

Controllability properties for the Navier–Stokes system are closely related to observability properties for the adjoint Oseen–Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, a new boundary ...

Given a level-one meromorphic linear differential system, we are interested in the behavior of its Stokes-Ramis matrices under the action of a holomorphic perturbation acting on the non-zero Stokes values. In particular, we show that the Stokes-Ramis matrices of the given system can be expressed as limit of convenient connection matrices of the perturbed systems. We believe that this result cou...

The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfyi...

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...