Introduction Relative pressure maps may be calculated from MRI velocity images on a voxel-by-voxel basis using the Navier-Stokes equation [1] to calculate the pressure gradient and numerical integration to generate a relative pressure map [3]. We show the accuracy of the derived pressure maps to be very sensitive to imaging noise and partial volume effects, both of which undermine the fluid dyn...

We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of...

In this paper, we consider the asymptotic behaviour of solutions for three-dimensional incompressible Navier-Stokes equations with nonlinear damping. We show the squeezing property and the existence of exponential attractor for this equation.

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

We characterize the solution of Navier-Stokes equation as a stochastic geodesic on the diffeomorphisms group, thus generalizing Arnold’s description of the Euler flow. Mathematics Subject Classification (2000). Primary 37L55; Secondary 35Q30, 58E30, 58J65, 60J60, 76D05.

We prove the strong Feller property and ergodicity for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Galerkin approximation approach.

Abstract. We propose a mathematical derivation of Brinkman’s force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Ω ⊂ R for the velocity field u of an incompressible fluid with kinematic viscosity ν and density 1. Brinkman’s force consists of a source term 6πνj where j is the curren...

This paper treats the homogeniza t ion of the Stokes or Navier-Stokes equat ions with a Dirichlet bounda ry condi t ion in a domain conta in ing many t iny solid obstacles, periodically dis tr ibuted in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of e a and are located at the nodes of a regular mesh of size e.) A suitable extension of the p...

It is shown that transition measures of the stochastic Navier-Stokes equation in 2D converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.

This paper reviews the recent progress on stochastic PDEs arising from different aspects of the turbulence theory including the stochastic Navier-Stokes equation, stochastic Burgers equation and stochastic passive scalar and passive vector equations. Issues discussed include the existence of invariant measures, scaling of the structure functions, asymptotic behavior of the probability density f...