An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, e...

We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The...

The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier–Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved...

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open and traction boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For this type of problem, the project...

The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier–Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved...

This paper is devoted to the existence of a weak solution system describing self-propelled motion rigid body in viscous fluid whole ℝ 3 . The modelled by incompressible nonhomogeneous Navier-Stokes with nonnegative density. described balance linear and angular momentum. We consider case where slip allowed at fluid-solid interface through Navier condition prove global solution.

In this article, we first consider some penalized finite element methods for the stationary Navier-stokes equations, based on the finite element space pair (Xh, Mh) which satisfies the discrete inf-sup condition for the P2−P0 element or does not satisfy the discrete inf-sup condition for the P1−P0 element. Then, we consider two-level penalty finite element methods which involve solving one smal...

In this paper, we consider a model equation for the Navier--Stokes strain equation. This has same identity enstrophy growth and number of regularity criteria as full Navier-Stokes equation, is also an evolution on constraint space. We prove finite-time blowup which shows that space are not sufficient their own to guarantee global Navier-Stokes. The mechanism self-amplification strain, consisten...