The Stokes and Navier-Stokes equations in an aperture domain

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Strong Solutions of the Navier-Stokes Equations in Aperture Domains

Stochastic Navier-stokes Equations

1. Stochastic Integration on Hilbert spaces 2 1.1. Gaussian measures on Hilbert spaces 2 1.2. Wiener processes on Hilbert spaces 6 1.3. Martingales on Banach spaces 7 1.4. Stochastic integration 8 1.5. Appendix: Stochastic integration w.r.t. cylindrical Wiener processes 12 2. Stochastic Di erential Equations on Hilbert spaces 13 2.1. Mild, weak and strong solutions 13 2.2. Existence and uniquen...

Quantum Navier–Stokes equations

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...

The Stationary Navier-Stokes Equations

Having considered the linear Stokes equations, we will now bring back the nonlinear term and consider the nonlinear version of the Stokes system. The solution of these equations can be viewed as the limit to which the solution of the full N-S equations tends as t tends to infinity. Of course no one knows at this point if the solutions of the N-S equations do tend to some limit as t tends to inf...