Related papers: Random attractors for the stochastic Navier--Stoke…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…
We consider a stochastic perturbation of the $\alpha$-Navier-Stokes model. The stochastic perturbation is an additive space-time noise of trace class. Under a natural condition about the trace of operator $Q$ in front of the noise, we prove…
The Navier--Stokes equation in the bidimensional torus is considered, with initial velocity and forcing term in suitable Besov spaces. Results of local existence and uniqueness are proven; under further restriction on the indexes defining…
The paper is devoted to studying the existence of a random attractor for stochastic porous media equations on infinite lattices under some conditions.
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…
This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\mathcal{A}_0$ in $H$…
We consider the Navier-Stokes equation on a two dimensional torus with a random force, white noise in time and analytic in space, for arbitrary Reynolds number $R$. We prove probabilistic estimates for the long time behaviour of the…
We consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation…
Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This…
We consider the incompressible, two dimensional Navier Stokes equation with periodic boundary conditions under the effect of an additive, white in time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we…
This paper derives the stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients. By means of weak convergence method and Stratonovich--Khasminskii averaging principle approach, the solution of two…
In this paper, we investigate both deterministic and stochastic 2D Navier Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev…
We extend our earlier \beta-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity…
The regularity of the global attractor of the incompressible Navier-Stokes equations for flows on two-dimensional domains is considered. It is assumed that domain $\Omega$ is a channel-like domain, i.e an arbitrary bounded or unbounded…
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…
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we…
In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results…
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…
A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear…
The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic…