Related papers: Lagrangian Navier-Stokes diffusions on manifolds: …
We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagrange multiplier. Moreover we describe how to obtain…
In this manuscript, we extend Constantin-Iyer's Lagrangian formulation of Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is naturally derived from a stochastic…
We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise.
This work presents an approach to the Navier-Stokes equations that is phrased in unbiased Eulerian coordinates, yet describes objects that have Lagrangian significance: particle paths, their dispersion and diffusion. The commutator between…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…
The stability of a two-dimensional viscous flow between two rotating porous cylinders is studied. The basic steady flow is the most general rotationally-invariant solution of the Navier-Stokes equations in which the velocity has both radial…
In this note, we prove the large deviation principle for the 2D-fractional stochastic Navier-Stokes equation on the torus under the dissipation order $ \alpha \in [\frac43, 2]$.
In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-$\alpha$ Navier-Stokes model on the two dimensional torus. We assume that the noise is a cylindrical Wiener process and its coefficient is…
The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations which have the same order and same solution…
The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…
Lagrangian tracer particle trajectories for invariant solutions of the Navier-Stokes equations confined to the three-dimensional geometry of plane Couette flow are studied. Treating the Eulerian velocity field of an invariant solution as a…
In this paper we consider the transport--Stokes system, which describes the sedimentation of particles in a viscous fluid in inertialess regime. We show existence of Lagrangian solutions to the Cauchy problem with $L^1$ initial data. We…
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density…
We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation…
We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical…
Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid…