Variational stokes

Error Estimator for Variational Consistentsurface Forces in Navier { Stokes

In coupled simulation of uid-structure phenomena the important unknowns for structural design are the interface forces caused by the dynamic uid pressure acting on the structure. Hence, the quality control of the numerical calculations have to be performed with the purpose of controlling the accuracy of the computed interface forces. We perform this control by (a) monitoring the global accuracy...

Lagrangian Navier-stokes Diffusions on Manifolds: Variational Principle and Stability

We prove a variational principle for stochastic flows on manifolds. It extends V. Arnold’s description of Lagrangian Euler flows, which are geodesics for the L2 metric on the manifold, to the stochastic case. Here we obtain stochastic Lagrangian flows with mean velocity (drift) satisfying the NavierStokes equations. We study the stability properties of such trajectories as well as the evolution...

A Variational Formulation for the Navier-stokes Equation

A variational approach to the Navier-Stokes equations

We propose a time discretization of the Navier-Stokes equations inspired by the theory of gradient flows. This discretization produces Leray/Hopf solutions in any dimension and suitable solutions in dimension 3. We also show that in dimension 3 and for initial datum in H, the scheme converges to strong solutions in some interval [0, T ) and, if the datum satisfies the classical smallness condit...

On a Variational Principle for the Navier-stokes Equation

In this paper we study the variational principle for the Navier-Stokes equation described in [Gom05], and clarify the role of boundary conditions. We show that in certain special cases this variational principle gives rise to new models for fluid equations.