WANG , Yejuan

This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite delays. The nonlinear terms of the equation are not expected to be Lipschitz continuous, but only satisfy continuity assumptions along with growth conditions, under which the uniqueness of the solutions may not hold. Using...

In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system is stable under perturbations, and that Morse...

A non-autonomous stochastic delay wave equation with linear memory and nonlinear damping driven by additive white noise is considered on the unbounded domain Rn. We establish the existence and uniqueness of a random attractor A that is compact in C([−h, 0]; H1 (Rn)) × C([−h, 0]; L2 (Rn)) × L2 µ(R+; H1 (Rn)) with 1 6 n 6 3.

In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the existence and uniqueness of mild solutions by using...

We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order p ≥ 2 driven by a tempered fractional Brownian motion (TFBM) Bσ,λ(t) with −1/2 < σ < 0 and λ > 0. First, the global existence and unique ness of mild solutions are established by using a new technical lemma for stochastic integrals...

In this paper, fractionally dissipative 2D quasi-geostrophic equations with an external force containing infinite delay is considered in the space Hs with s ≥ 2 − 2α and α ∈ ( 1 2 , 1). First, we investigate the existence and regularity of solutions by Galerkin approximation and the energy method. The continuity of solutions with respect to...

In this paper we investigate the regularity of global attractors and of exponential attractors for two dimensional quasi-geostrophic equations with fractional dissipation in H2α+s (T 2 ) with α > 1 2 and s > 1. We prove the exis tence of (H2α−+s (T 2 ), H2α+s (T 2 ))-global attractor A, that is, A is compact in H2α+s (T 2 ) and attracts all...

In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t)BQσ,λ(t) with −1/2<σ<0−1/2<σ<0 and λ>0λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the existence and uniqueness of mild...

In this paper, we study the full compressible Navier--Stokes system in a bounded domain Ω⊂R3 , where the viscosity and heat conductivity depend on temperature in a power law (θb for some constant b>0 ) of Chapman--Enskog. We obtain the local existence of strong solution to the initial-boundary value problem (IBVP), which is not trivial,...

On the one hand, the primitive three-dimensional viscous equations for large-scale ocean and atmosphere dynamics are commonly used in weather and climate predictions. On the other hand, ever since the middle of the last century, it has been widely recognized that the climate variability exhibits long-time memory. In this paper, we first prove...

The polynomial stability problem of stochastic delay differential equations has been studied in recent years. In contrast, there are relatively few works on stochastic partial differential equations with pantograph delay. The present paper is devoted to investigating large-time asymptotic properties of solutions for stochastic pantograph delay...