On a Variational Principle for the Navier-stokes Equation

Investigation of instable fluid velocity in pipes with internal nanofluid flow based on Navier-Stokes equations

In this article, the instable fluid velocity in the pipes with internal nanofluid is studied. The fluid is mixed by SiO2, AL2O3, CuO and TiO2 nanoparticles in which the equivalent characteristic of nanofluid is calculated by rule of mixture. The force induced by the nanofluid is assumed in radial direction and is obtained by Navier-Stokes equation considering viscosity of nanofluid. The displac...

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...

Anti-Symmetric Hamiltonians (II): Variational resolutions for Navier-Stokes and other nonlinear evolutions

The nonlinear selfdual variational principle established in the first part of this paper [8] – though good enough to be readily applicable in many stationary nonlinear partial differential equations – did not however cover the case of nonlinear evolutions such as the Navier-Stokes equations. One of the reasons is the prohibitive coercivity condition that is not satisfied by the corresponding se...

On a p(x)-Kirchho equation via variational methods

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

A Variational Formulation for the Navier-stokes Equation