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Anhui Gu

Publications and source records attributed to Anhui Gu.

10 recordsLinked to original sources
arXiv2025

Pullback $V$-Attractors of the Stochastic Calmed 3$D$ Navier-Stokes Equations

In this paper, we investigate a calmed version of the 3$D$ rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin approximation, we establish the global well-posedness of solutions for the calmed system. Then, we demonstrate the existence of a closed, measurable $\mathcal{D}_V$-pullback absorbing set. Finally, by proving the pullback flattening property, we obtain the existence of a $\mathcal{D}_V$-pullback attractor in \(V\).

math.AP↗
arXiv2020

Weak Pullback Mean Random Attractors for Stochastic Evolution Equations and Applications

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction-diffusion equations, the stochastic $p$-Laplace equation and stochastic porous media equations are established.

math.AP↗
arXiv2020

Rough Path Theory to approximate Random Dynamical Systems

We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm \om=(\omega,\bbomega)$ is a rough path defined by a Brownian motion $\omega$ on $\RR^m$. Under the usual regularity assumption on $f$, namely $f\in C^3_b (\RR^d, \RR^{d\times m})$, the rough differential equation has a unique solution that defines a random dynamical system $\phi_0$. On the other hand, we also consider an ordinary random differential equation $dY_\delta=f(Y_\delta)d\omega_\de$, where $\omega_\de$ is a random process with stationary increments and continuously differentiable paths that approximates $\omega$. The latter differential equation generates a random dynamical system $\phi_\delta$ as well. We show the convergence of the random dynamical system $\phi_\delta$ to $\phi_0$ for $\delta\to 0$ in H\"older norm.

math.PR↗
arXiv2015

Regularity of pullback attractors and equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains

A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, it is showed that every generated random cocycle has a pullback attractor in $L^l(\mathbb{R}^N)\times L^2(\mathbb{R}^N)$ with $l\in(2,p]$, and the family of obtained attractors is upper semi-continuous at any intensity of noise. Moreover, if some additional conditions are added, then the system possesses a unique equilibrium and is attracted by a single point.

math.AP↗
arXiv2014

Random Attractors of Stochastic Lattice Dynamical Systems Driven by Fractional Brownian Motions and its Erratum

This paper is devoted to considering the stochastic lattice dynamical systems (SLDS) driven by fractional Brownian motions with Hurst parameter bigger than $1/2$. Under usual dissipativity conditions these SLDS are shown to generate a random dynamical system for which the existence and unique of a random attractor is established. Furthermore, the random attractor is in fact a singleton sets random attractor. Next, we give an erratum because of the misused theory.

math.DS↗
arXiv2014

Singleton sets random attractor for stochastic FitzHugh-Nagumo lattice equations driven by fractional Brownian motions

The paper is devoted to the study of the dynamical behavior of the solutions of stochastic FitzHugh-Nagumo lattice equations, driven by fractional Brownian motions, with Hurst parameter greater than $1/2$. Under some usual dissipativity conditions, the system considered here features different dynamics from the same one perturbed by Brownian motion. In our case, the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.

math.DS↗
arXiv2014

Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both deterministic non-autonomous forcing terms and multiplicative white noise. Our results recover many existing ones on the existences of pullback attractors for lattice dynamical systems with autonomous terms or white noises.

math.DS↗
arXiv2013

Synchronization of Coupled Stochastic Systems Driven by Non-Gaussian Lévy Noises

We consider the synchronization of the solutions to coupled stochastic systems of $N$-stochastic ordinary differential equations (SODEs) driven by Non-Gaussian Lévy noises ($N\in \mathbb{N})$. We discuss the synchronization between two solutions and among different components of solutions under certain dissipative and integrability conditions. Our results generalize the present work obtained in Liu et al (2010) and Shen et al (2010).

math.DS↗