scholarly journals Long-time behavior of 3D stochastic planetary geostrophic viscous model

2018 ◽  
Vol 18 (05) ◽  
pp. 1850038
Author(s):  
Zhao Dong ◽  
Rangrang Zhang
Keyword(s):  
Hausdorff Dimension ◽  
Invariant Measure ◽  
Random Noise ◽  
Random Attractor ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Exponential Mixing ◽  
Model Driven ◽  
Long Time ◽  
Mixing Property

In this paper, we consider the 3D planetary geostrophic viscous model driven by an additive random noise. It is proved that this model has exponential mixing property and global random attractor at the same time. Further, we deduce that the support of the integration of the invariant measure for the dynamic generated by this model is exactly a minimal global random attractor. Moreover, we show that the global random attractor has finite Hausdorff dimension.

scholarly journals A Stochastic Weakly Damped, Forced KdV-BO Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guolian Wang
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Global Solution ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Energy Type ◽  
Bo Equation

We investigate the long time behavior of the damped, forced KdV-BO equation driven by white noise. We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the spaceH1(ℝ).

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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