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We consider a stochastic system of $N$ particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
We consider an optimal control problem for the Navier-Stokes system with Navier slip boundary conditions. We denote by $\alpha$ the friction coefficient and we analyze the asymptotic behavior of such a problem as $\alpha\to \infty$. More…
We study the $L^{\infty}$ stability of the 2D Navier-Stokes equations with a viscosity-dependent Navier boundary condition around shear profiles which are linearly unstable for the Euler equation. The dependence from the viscosity is given…
We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck equation coupled with the compressible isentropic Navier-Stokes system through a drag force…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the…
The asymptotic behavior of solutions to the second order elliptic equations in exterior domains is studied. In particular, under the assumption that the solution belongs to the Lorentz space $L^{p,q}$ or the weak Lebesgue space…
We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain…
We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…
We prove that given initial data $\omega_0\in L^\infty(\mathbb{T}^2)$, forcing $g\in L^\infty(0,T; L^\infty(\mathbb{T}^2))$, and any $T>0$, the solutions $u^\nu$ of Navier-Stokes converge strongly in $L^\infty(0,T;W^{1,p}(\mathbb{T}^2))$…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each…
We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…
In this paper, we study the asymptotic behavior of solutions to the compressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length…
We consider the incompressible Navier-Stokes equations in a bounded domain with $\mathcal{C}^{1,1}$ boundary, completed with slip boundary condition. Apart from studying the general semigroup theory related to the Stokes operator with…
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…
This study is devoted to the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains. First, the main results on the construction of the weak solutions and on their asymptotic behavior are reviewed and…
We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero (in any arbitrarily…
In this paper, we establish the vanishing viscosity limit result of the 2D stationary Navier-Stokes equations outside a rotating disc. On the boundary of the disc, the fluid is subjected to a small perturbation of a non zero rotation of…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…