Related papers: Statistical properties of stochastic 2D Navier-Sto…
The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…
We propose a two-dimensional generalization of Constantin-Lax-Majda model [2]. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line…
Continuous data assimilation methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT) [2], are known to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
We introduce a modification of the Navier-Stokes equation that has the remarkable property of possessing an infinite number of conserved quantities in the inviscid limit. This new equation is studied numerically and turbulence properties…
We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the…
We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously…
In this paper we prove the existence of random attractors for the Navier--Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.
The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of passively advected vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The…
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…
The ergodic properties of the randomly forced Navier-Stokes system have been extensively studied in the literature during the last two decades. The problem has always been considered in bounded domains, in order to have, for example,…
We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…
This paper concerns the Cauchy problem in R^d for the stochastic Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+ [(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad divu=0, driven by white noise \dot…
We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure…
In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the…
A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…
New explicit solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{2}\setminus\left\{ \boldsymbol{0}\right\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant…
In this paper, we establish ergodic and mixing properties of stochastic 2D Navier-Stokes equations driven by a highly degenerate multiplicative Gaussian noise. The noise could appear in as few as four directions and the intensity of the…