Related papers: Stochastic homogenization for two dimensional Navi…
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…
These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested…
We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to…
This article is devoted to a regularity criteria for solutions of the Navier-Stokes equations in terms of regularity along the stream lines. More precisely, we prove that a suitable weak solution for the Navier-Stokes equations is regular…
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…
In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…
The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…
The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first establish the $L^q_t(L^p)$-maximal regularity estimate for…
The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential…
For linearized Navier-Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability…
We consider the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance relation for this system holds for weak…
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…
In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully discrete problem, where a discontinuous Galerkin method in time…
We show the existence of (a class of) weak solutions to the three-dimensional stationary incompressible inhomogeneous Navier--Stokes equations with density-dependent viscosity coefficient in the axially symmetric case. Further symmetric…
Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \mathbf{W}^{-1,p}(\Omega))$ for $p$ and $q$ in appropriate parameter ranges are proven. The case of spatially…
We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…