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We study a two-dimensional Navier--Stokes system with anisotropic viscosity, linear damping term, and an additive noise on the whole space $\mathbb{R}^2$. For this model we prove uniqueness of invariant measures when the damping coefficient…

Probability · Mathematics 2026-01-29 Siyu Liang

In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role.

Probability · Mathematics 2017-06-28 Jianliang Zhai , Tusheng Zhang , Wuting Zheng

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The…

Probability · Mathematics 2009-04-06 Mauro Mariani

The aim of this paper is threefold. Firstly, we prove the existence and the uniqueness of a global strong (in both the probabilistic and the PDE senses) $\mathrm{H}^{1}_2$-valued solution to the 2D stochastic Navier-Stokes equations (SNSEs)…

Probability · Mathematics 2021-10-06 Zdzislaw Brzezniak , Xuhui Peng , Jianliang Zhai

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

Probability · Mathematics 2026-02-23 Esmée Theewis , Mark Veraar

We consider the globally modified stochastic (hyperviscous) Navier-Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of the weak solutions, and then show their convergence to the…

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

In this paper, we establish a small time large deviation principles for scalar stochastic conservation laws driven by multiplicative noise. The doubling of variables method plays a key role.

Probability · Mathematics 2020-04-08 Zhao Dong , Rangrang Zhang

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…

Probability · Mathematics 2025-12-12 Huijie Qiao

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under…

Probability · Mathematics 2025-09-30 Huijie Qiao

We study large deviations from the invariant measure for nonlinear Schr\"odinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jak\v{s}i\'{c} et al., Comm. Pure Appl.…

Analysis of PDEs · Mathematics 2026-02-03 Yuxuan Chen , Shengquan Xiang

This article develops the viscosity solution approach to the large deviation principle for the following two- and three-dimensional stochastic convective Brinkman-Forchheimer equations on the torus $\mathbb{T}^d,\ d\in\{2,3\}$ with small…

Probability · Mathematics 2025-10-02 Sagar Gautam , Manil T. Mohan

We study the small noise asymptotics for two-dimensional Navier-Stokes equa- tions driven by Levy noise. Central limit theorem and moderate deviation are established under appropriate assumptions, which describes the exponen- tial rate of…

Probability · Mathematics 2017-11-28 Ran Wang , Jianliang Zhai

The paper is devoted to studying the asymptotics of the family $(\mu^\varepsilon)$ of stationary measures of the Markov process generated by the flow of stochastic 2D Navier-Stokes equation with smooth white noise. By using the large…

Analysis of PDEs · Mathematics 2016-02-23 Davit Martirosyan

We consider the incompressible 2D Navier-Stokes equations on the torus, driven by a deterministic time periodic force and a noise that is white in time and degenerate in Fourier space. The main result is twofold. Firstly, we establish a…

Probability · Mathematics 2023-07-13 Rongchang Liu , Kening Lu

We study the large deviations principle (LDP) of Donsker-Varadhan type for the white-forced Navier-Stokes system in a bounded domain. Under the assumption that the noise is non-degenerate, we establish level-2 and level-3 LDPs with rate…

Analysis of PDEs · Mathematics 2025-06-18 Meng Zhao

We review some basic results on existence and uniqueness of the invariant measure for the two-dimensional stochastic Navier-Stokes equations. A large part of the literature concerns the additive noise case; after revising these models, we…

Probability · Mathematics 2025-01-06 Benedetta Ferrario , Margherita Zanella

We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity…

Probability · Mathematics 2016-09-15 Z. Brzeźniak , B. Goldys , T. Jegaraj

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.

Probability · Mathematics 2016-06-08 Jie Xiong , Jianliang Zhai

A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…

Statistics Theory · Mathematics 2010-02-24 Amarjit Budhiraja , Paul Dupuis , Vasileios Maroulas

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

Probability · Mathematics 2016-11-01 Yumeng Li , Ran Wang , Nian Yao , Shuguang Zhang