A variational principle for the Navier-Stokes equation

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.

A Variational Formulation for the Navier-stokes Equation

Stochastic Least-Action Principle for the Incompressible Navier-Stokes Equation

We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton’s principle for the incompressible Euler solutions in the case of zero viscosity. We use this principle to give a new derivation of a stochastic Kelvin Theorem for the Navier-Stokes equation, recently established by Constantin and Iyer, which shows that...

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...

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...