相关论文: On a critical Leray$-\alpha$ model of turbulence
In this paper, we establish the existence of a unique "regular" weak solution to turbulent flows governed by a general family of $\alpha$ models with critical regularizations. In particular this family contains the simplified Bardina model…
In 1934 J. Leray proposed a regularization of the Navier-Stokes equations whose limits were weak solutions of the NSE. Recently, a modification of the Leray model, called the Leray-alpha model, has atracted study for turbulent flow…
We consider a family of Leray-$\alpha$ models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter $\theta$, of the Navier-Stokes equations. In particular, they share…
Rates of convergence of solutions of various two-dimensional $\alpha-$regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the $L^\infty$-$L^2$ time-space norm,…
In this paper, we establish the existence and the regularity of a unique weak solution to turbulent flows in a bounded domain ${\Omega}\subset \mathbb R^3$ governed by the so-called Leray-{\alpha} model. We consider the Navier slip boundary…
In this paper, we investigate some priori estimates to provide the critical regularity criteria for incompressible Navier-Stokes equations on $\mathbb{R}^3$ and super critical surface quasi-geostrophic equations on $\mathbb{R}^2$.…
In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier--Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria…
In this paper, we establish the global well-posedness of stochastic 3D Leray-$\alpha$ model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equation regularized through a…
This paper deals with the distributed and boundary controllability of the so called Leray-$\alpha$ model. This is a regularized variant of the Navier-Stokes system ($\alpha$ is a small positive parameter) that can also be viewed as a model…
The Navier-Stokes-$\alpha$ equations belong to the family of LES (Large Eddy Simulation) models whose fundamental idea is to capture the influence of the small scales on the large ones without computing all the whole range present in the…
Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply…
It has recently become common to study many different approximating equations of the Navier-Stokes equation. One of these is the Leray-$\alpha$ equation, which regularizes the Navier-Stokes equation by replacing (in most locations) the…
We demonstrate that the problem of existence of Leray self-similar blow up solutions in a generalized mild Navier-Stokes system with the fractional Laplacian $(-\Delta)^{\gamma/2}$ can be stated as a fixed point problem for a…
In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the…
We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of…
Let $v$ be the velocity of Leray-Hopf solutions to the axially symmetric three-dimensional Navier-Stokes equations. It is shown that $v$ is regular if the angular velocity $v_\theta$ satisfies an integral condition which is critical under…
In this paper, we show the global regularity and the optimal decay of weak solutions to the generalized Leray problem with critical dissipation. Our method is based on the maximal smoothing effect, $L^{p}$-type elliptic regularity of…
We explore one-point and two-point statistics of the Navier-Stokes-alpha-beta regularization model at moderate Reynolds number in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier-Stokes-alpha model…
The Leray-$\alpha$ model reduces the range of active scales of the Navier-Stokes equations by smoothing the advective transport. Here we assess the potential of the Leray-$\alpha$ model in its standard formulation to simulate wall-bounded…
We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$\Delta$) $\alpha$/2 in the diffusion term. In the…