Related papers: The Small Scales of the Stochastic Navier Stokes E…
We study the qualitative properties of solutions to the 2D stochastic Navier-Stokes equations with forcing that is white in time and coloured in space. Our main result shows that the unique invariant measure of this system is equivalent to…
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model…
We consider the incompressible 2D Navier-Stokes equations with periodic boundary conditions driven by a deterministic time periodic forcing and a degenerate stochastic forcing. We show that the system possesses a unique ergodic periodic…
We introduce and analyze a space-time least-squares method associated to the unsteady Navier-Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess,…
We study the two-dimensional Navier-Stokes system on a flat cylinder with the usual Dirichlet boundary conditions for the velocity field u. We formulate the problem as an infinite system of ODE's for the natural Fourier components of the…
Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…
We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found…
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or…
Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally-truncated Euler equation. Using direct numeric…
We study the solution $u_\varepsilon$ to the Navier-Stokes equations in $\mathbb R^3$ perforated by small particles centered at $(\varepsilon \mathbb Z)^3$ with no-slip boundary conditions at the particles. We study the behavior of…
In this paper, we introduce the Fourier-restricted Euler and hypodissipative Navier--Stokes equations. These equations are analogous to the Euler and hypodissipative Navier--Stokes equations respectively, but with the Helmholtz projection…
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a…
The predictability of turbulent flows remains a challenging problem for mathematicians, physicists, and meteorologists. In this context, we consider the 3D incompressible Navier-Stokes equations with small-scale random forcing on…
We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for $\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme…
The flow of a viscous fluid is perturbed by its internal friction which generates heat and leads to a small temperature change. This does not occur for an ideal fluid. We would like to resolve this picture as a function of the dynamical…
Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The Large Eddy Simulations (LES) models are efficient tools to approximate turbulent fluids and an important step in the…
This paper deals with the approximation of the weak solutions of the incompressible Navier Stokes Fourier system. In particular it extends the artificial compressibility method for the Leray weak solutions of the Navier Stokes equation,…
Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energy equality for weak solutions in a large class of function…
This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays,…
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…