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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…

Numerical Analysis · Mathematics 2022-05-02 Jad Doghman

In this paper, we are interested in the long-time behaviour of stochastic systems of n interacting vortices: the position in R2 of each vortex evolves according to a Brownian motion and a drift summing the influences of the other vortices…

Probability · Mathematics 2015-01-27 Joaquin Fontbona , Benjamin Jourdain

We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…

Analysis of PDEs · Mathematics 2017-01-03 Dominic Breit , Martina Hofmanová

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. The dissipative character of our model…

Analysis of PDEs · Mathematics 2017-12-06 Francesco Di Plinio , Andrea Giorgini , Vittorino Pata , Roger Temam

In this paper, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability of the original equation. The central idea is to extract a…

Numerical Analysis · Mathematics 2024-10-29 Chuchu Chen , Tonghe Dang , Jialin Hong , Fengshan Zhang

We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…

Analysis of PDEs · Mathematics 2024-07-23 Ziyu Liu , Dongyi Wei , Shengquan Xiang , Zhifei Zhang , Jia-Cheng Zhao

We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…

Statistics Theory · Mathematics 2019-04-05 Igor Cialenco , Hyun-Jung Kim , Sergey V. Lototsky

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\alpha/2$-subordinated cylindrical Brownian motions with $\alpha\in(1,2)$. To prove the results, we truncate the…

Probability · Mathematics 2015-06-11 Zhao Dong , Lihu Xu , Xicheng Zhang

We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the…

Numerical Analysis · Mathematics 2025-12-01 Jun Wang , Jie Su , Leslie Greengard , Shidong Jiang , Shravan Veerapaneni

We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear…

Analysis of PDEs · Mathematics 2023-11-01 Elie Abdo , Ruimeng Hu , Quyuan Lin

In this paper we establish local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is…

Probability · Mathematics 2013-03-26 Wei Liu , Michael Röckner

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…

Numerical Analysis · Mathematics 2019-07-10 Dominic Breit , Alan Dodgson

The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…

Dynamical Systems · Mathematics 2009-11-13 Ray Nagem , Guido Sandri , David Uminsky , C. Eugene Wayne

The paper is concerned with the analysis of an evolutionary model for magnetoviscoelastic materials in two dimensions. The model consists of a Navier-Stokes system featuring a dependence of the stress tensor on elastic and magnetic terms, a…

Analysis of PDEs · Mathematics 2019-04-16 Martin Kalousek , Joshua Kortum , Anja Schlömerkemper

We analyze the explosion problem for a class of stochastic models introduced in Part I (arXiv:2103.06912), referred to as doubly stochastic Yule cascades. These models arise naturally in the construction of solutions to evolutionary PDEs as…

Probability · Mathematics 2021-12-06 Radu Dascaliuc , Tuan N. Pham , Enrique Thomann , Edward C. Waymire

We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of…

Probability · Mathematics 2013-07-30 H. Bessaih , B. Ferrario

Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…

Probability · Mathematics 2022-04-20 Sima Mehri , Erfan Salavati , Bijan Z. Zangeneh

In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…

Numerical Analysis · Mathematics 2025-12-30 Endre Süli , Dennis Trautwein

The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional…

Probability · Mathematics 2014-10-28 Xin Thomson Tong , Ramon van Handel

In this paper the inverse scattering problem for the nonstationary Dirac-type system on the whole plane was considered. A nonlinear evolution sytem of equation related to nonstationary Dirac-type system is introduced and the solviblity of…

Mathematical Physics · Physics 2009-08-20 Mansur I Ismailov