Related papers: From additive to transport noise in 2D fluid dynam…
Asymptotic random dynamics of weak solutions for a damped stochastic wave equation with the nonlinearity of arbitrarily large exponent and the additive noise on $\mathbb{R}^n$ is investigated. The existence of a pullback random attractor is…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
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…
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…
Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
The transport phenomenon of active particles confined in 3D(three dimensional) corrugated confined channel with Gaussian noises is investigated. Large noise intensity perpendicular to the symmetry axis is good for the diffusion and current…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
We study inviscid limits of invariant measures for the 2D Stochastic Navier-Stokes equations. As shown in \cite{Kuksin2004} the noise scaling $\sqrt{{\nu}}$ is the only one which leads to non-trivial limiting measures, which are invariant…
We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength…
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…
How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…
This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
We derive equations for fluid dynamics from a non-extensive Boltzmann transport equation consistent with Tsallis' non-extensive entropy formula. We evaluate transport coefficients employing the relaxation time approximation and investigate…
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…
We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low…
Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of $k$-forms, which arises naturally in geometric…
This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach,…