182 citations · 1.5k across the 227 of their papers we have counts for
10 papers · 2 filters
Invariant manifolds for stochastic partial differential equations
Jinqiao Duan, Kening Lu, Bjoern Schmalfuss
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite…
Smooth stable and unstable manifolds for stochastic partial differential equations
Jinqiao Duan, Kening Lu, Bjorn Schmalfuss
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dime…
Determining functionals for random partial differential equations
Igor Chueshov, Jinqiao Duan, Björn Schmalfuß
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite…
Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations
David Cheban, Jinqiao Duan
The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is for…
Generalization of the Second Bogolyubov's Theorem for Non-Almost Periodic Systems
David N. Cheban, Jinqiao Duan, Anatoly Gherco
The article is devoted to the generalization of the second Bogolyubov's theorem to non-almost periodic dynamical systems. We prove the analog of the second Bogolyubov's theorem for…
Stochastic Dynamics of a Coupled Atmosphere--Ocean Model
J. Duan, H. Gao, B. Schmalfuss
The investigation of the coupled atmosphere-ocean system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which…
Dynamics of a Coupled Atmosphere-Ocean Model
Hongjun Gao, Jinqiao Duan
We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air-sea interface. First, we show that the coupled a…
A Markov jump process approximation of the stochastic Burgers equation
Christoph Gugg, Jinqiao Duan
We consider the stochastic Burgers equation $ \dnachd{t} ψ(t,r) = Δψ(t,r) + \nabla ψ^2(t,r)+\sqrt{γψ(t,r)} η(t,r) $ with periodic boundary conditions, where $r \in [0,1]…
Ergodic Dynamics of the Stochastic Swift-Hohenberg System
Wei Wang, Jianhua Sun, Jinqiao Duan
The Swift-Hohenberg fluid convection system with both local and nonlocal nonlinearities under the influence of white noise is studied. The objective is to understand the difference…
Ergodic Dynamics of the Coupled Quasigeostrophic Flow-Energy Balance System
Aijun Du, Jinqiao Duan, Hongjun Gao +1
The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic flow-energy balance model. This model consists of the large…