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Related papers: Eddy viscosity by L\'evy transport noises

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The paper is devoted to the open problem of regularization by noise of 3D Navier-Stokes equations. Opposite to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of…

Probability · Mathematics 2021-08-11 Franco Flandoli , Dejun Luo

We prove that a version of Smagorinsky Large Eddy model for a 2D fluid in vorticity form is the scaling limit of suitable stochastic models for large scales, where the influence of small turbulent eddies is modeled by a transport type…

Probability · Mathematics 2023-02-28 Franco Flandoli , Dejun Luo , Eliseo Luongo

We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely,…

Probability · Mathematics 2014-05-05 Fernanda Cipriano , Iván Torrecilla

We establish scaling limit results for fluid dynamics equations driven by pseudo-transport noise. The behaviour of noise at small scales is governed by a parameter a. This extends previous results by Flandoli and Luo (2020) and Galeati…

Probability · Mathematics 2026-05-28 Shuaijie Jiao , Marco Romito

The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids.…

Nuclear Theory · Physics 2009-01-14 Paul Romatschke

In this paper, we consider stochastic two-phase Stefan problem driven by general jump L\'evy noise. We first obtain the existence and uniqueness of the strong solution and then establish the ergodicity of the stochastic Stefan problem.…

Probability · Mathematics 2024-08-05 Xiaotian Ge , Shijie Shang , Jianliang Zhai , Tusheng Zhang

We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the…

Probability · Mathematics 2026-01-30 Benjamin Gess , Rishabh S. Gvalani , Adrian Martini

We consider the vorticity form of 2D Navier--Stokes equations perturbed by an Ornstein--Uhlenbeck flow of transport type. Contrary to previous works where the random perturbation was interpreted as Stratonovich transport noise, here we…

Probability · Mathematics 2025-01-22 Chang Liu , Dejun Luo

We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved…

Probability · Mathematics 2024-09-27 Zdzisław Brzeźniak , Matteo Ferrari

The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with $L^p$…

Analysis of PDEs · Mathematics 2024-10-10 Gennaro Ciampa , Gianluca Crippa , Stefano Spirito

In this paper we prove that the stochastic Navier-Stokes equations with stable L\'evy noise generates a random dynamical systems. Then we prove the existence of random attractor for the Navier-Stokes equations on 2D spheres under stable…

Probability · Mathematics 2019-10-22 Leanne Dong

We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…

Analysis of PDEs · Mathematics 2017-12-06 Peter Constantin , Vlad Vicol

Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…

Probability · Mathematics 2012-09-03 Elżbieta Motyl

In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is…

Probability · Mathematics 2018-01-26 Wuting Zheng , Jianliang Zhai , Tusheng Zhang

In this paper, we first explore certain structural properties of L\'evy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by L\'evy noise.…

Probability · Mathematics 2022-11-15 Arvind Kumar Nath , Suprio Bhar

In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem…

Analysis of PDEs · Mathematics 2009-02-13 Christophe Lacave

In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative $L\acute{e}vy$ noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in…

Probability · Mathematics 2015-05-19 Zhao Dong , Jie Xiong , Jianliang Zhai , Tusheng Zhang

We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$.…

Probability · Mathematics 2020-04-22 Hakima Bessaih , Benedetta Ferrario

We consider the Navier-Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting velocity field by space-time dependent noise…

Analysis of PDEs · Mathematics 2018-08-02 Martina Hofmanová , James-Michael Leahy , Torstein Nilssen

In this paper, we establish a moderate deviation principle for an abstract nonlinear equation forced by random noise of L\'evy type. This type of equation covers many hydrodynamical models, including stochastic 2D Navier-Stokes equations,…

Probability · Mathematics 2025-02-12 Yue Li , Shijie Shang