Related papers: Stochastic 3D Leray-$\alpha$ Model with Fractional…

We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are taken in equivalent inner products, defined through powers…

This paper concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we prove that there exist distinct Leray solutions in the…

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…

In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $\alpha|u|^{\beta-1}u(\alpha>0,\;\beta\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, 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…

Let $d \geq 3$. We consider the global Cauchy problem for the generalised Navier-Stokes system \partial_t u + (u \cdot \nabla) u &= - D^2 u - \nabla p \nabla \cdot u &= 0 u(0,x) &= u_0(x) for $u: \R^+ \times \R^d \to \R^d$ and $p: \R^+…

We consider the 3D stochastic Navier-Stokes equations (NSE) on torus where the viscosity exponent can be larger than the Lions exponent 5/4. For arbitrarily prescribed divergence-free initial data in $L^{2}_x$, we construct infinitely many…

Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator…

We study the three-dimensional incompressible Navier-Stokes system on $\mathbb{R}^3$ with an additional dissipative nonlocal term \[ \partial_t u + (u\cdot\nabla)u + \nabla p = \nu \Delta u + Lu, \qquad {\rm div}\, u = 0, \] where $L$ is a…

In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…

This paper concerns the 3-dimensional Lagrangian Navier-Stokes $\alpha$ model and the limiting Navier-Stokes system on smooth bounded domains with a class of vorticity-slip boundary conditions and the Navier-slip boundary conditions. It…

In this work we study the 3D Navier-Stokes equations, under the action of an external force and with the fractional Laplacian operator $(-\Delta)^{\alpha}$ in the diffusion term, from the point of view of variable Lebesgue spaces. Based on…

We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only…

We investigate existence, Liouville type theorems and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power…

In this paper, we study the global regularity of strong solution to the Cauchy problem of 3D incompressible Navier-Stokes equations with large data and non-zero force. We prove that the strong solution exists globally for $\nabla u\in…

A global time-discretized scheme for the Navier-Stokes equation system in its Leray projection form is defined. It is shown that the scheme converges to a bounded global classical solution for smooth data which have polynomial decay at…

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…

In this paper, we study the 3D regularized Boussinesq equations. The velocity equation is regularized \`a la Leray through a smoothing kernel of order $\alpha$ in the nonlinear term and a $\beta$-fractional Laplacian; we consider the…

We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction…

We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…