13 citations · 28 across the 9 of their papers we have counts for
9 papers
Wong-Zakai type approximations of rough random dynamical systems by smooth noise
Qiyong Cao, Hongjun Gao, Bjorn Schmalfuss
This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by a geometric fractional Brownian rough path $\bold…
Rough Path Theory to approximate Random Dynamical Systems
Hongjun Gao, María J. Garrido-Atienza, Anhui Gu +2
We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm \om=(ω,\bbomega)$ is a rough path defined by a Brownian motion on $\RR^m$. Under the usual regularity a…
On 3D Navier-Stokes equations: regularization and uniqueness by delays
Hakima Bessaih, María J. Garrido-Atienza, Björn Schmalfuss
A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term…
Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces
María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss
In this paper we investigate the existence and some useful properties of the Lévy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motio…
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
Hakima Bessaih, María J. Garrido-Atienza, Björn Schmalfuss
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter…
Pathwise solutions to stochastic partial differential equations driven by fractional Brownian motions with Hurst parameters in
María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss
Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a Hölder continuous function with…
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…
Probabilistic Dynamics of Two-Layer Geophysical Flows
Igor Chueshov, Jinqiao Duan, Bjorn Schmalfuss
The two-layer quasigeostrophic flow model is an intermidiate system between the single-layer 2D barotropic flow model and the continuously stratified, 3D baroclinic flow model. Thi…
The 3D Quasigeostrophic Fluid Dynamics under Random Forcing on Boundary
Jinqiao Duan, Bjorn Schmalfuss
The three-dimensional baroclinic quasigeostrophic flow model has been widely used to study basic mechanisms in oceanic flows and climate dynamics. In this paper, we consider this f…