An Eulerian-Lagrangian Approach¶to the Navier-Stokes Equations

An Eulerian-Lagrangian approach to the Navier-Stokes equations

We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

0 An Eulerian - Lagrangian Approach to the Navier - Stokes equations

Lagrangian Structures for the Stokes, Navier-stokes and Euler Equations

— We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [6].

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...

Semi-Lagrangian exponential integrators for the incompressible Navier-Stokes equations

preprint numerics no. 7/2011 norwegian university of science and technology trondheim, norway Direct applications of high order DIRK-CF methods as presented in [7] to the incompressible Navier-Stokes equations were found to yield a loss in order of convergence. The DIRK-CF methods are exponential integrators arising from the IMEX Runge-Kutta techniques proposed in [1], and are semi-Lagrangian w...