scholarly journals Pullback dynamics of a 3D modified Navier-Stokes equations with double delays

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pan Zhang ◽  
Lan Huang ◽  
Rui Lu ◽  
Xin-Guang Yang
Keyword(s):  
Time Delays ◽  
Energy Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Convergence Method ◽  
Double Time ◽  
External Forces ◽  
Weak Convergence Method

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback dynamics for a 3D modified Navier-Stokes equations with double time-delays, which includes delays on external force and convective terms respectively. Based on the property of monotone operator and some suitable hypotheses on the external forces, the existence and uniqueness of weak solutions can be shown in an appropriate functional Banach space. By using the energy equation technique and weak convergence method to achieve asymptotic compactness for the process, the existence of minimal family of pullback attractors has also been derived.</p>

scholarly journals Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei Shi ◽  
Xiaona Cui ◽  
Xuezhi Li ◽  
Xin-Guang Yang
Keyword(s):  
Time Delays ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Subcritical Nonlinearity ◽  
Double Time ◽  
Autonomous Dynamical Systems

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the control in engineer and application. Based on the existence of weak and strong solutions for three dimensional hydrodynamical model with subcritical nonlinearity, we proved the existence of minimal family for pullback attractors with respect to tempered universes for the non-autonomous dynamical systems.</p>

The non-Lipschitz stochastic Cahn–Hilliard–Navier–Stokes equations in two space dimensions

2021 ◽  
pp. 2250003
Author(s):  
Chengfeng Sun ◽  
Qianqian Huang ◽  
Hui Liu
Keyword(s):  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates ◽  
Convergence Method ◽  
Two Space Dimensions ◽  
Lipschitz Conditions ◽  
Weak Convergence Method

The stochastic two-dimensional Cahn–Hilliard–Navier–Stokes equations under non-Lipschitz conditions are considered. This model consists of the Navier–Stokes equations controlling the velocity and the Cahn–Hilliard model controlling the phase parameters. By iterative techniques, a priori estimates and weak convergence method, the existence and uniqueness of an energy weak solution to the equations under non-Lipschitz conditions have been obtained.

Large deviation principles of 2D stochastic Navier–Stokes equations with Lévy noises

2021 ◽  
pp. 1-49
Author(s):  
Huaqiao Wang
Keyword(s):  
Weak Convergence ◽  
Stokes Equations ◽  
Large Deviation ◽  
Careful Analysis ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convergence Method ◽  
Weak Convergence Method ◽  
Weak Convergence Approach

Taking the consideration of two-dimensional stochastic Navier–Stokes equations with multiplicative Lévy noises, where the noises intensities are related to the viscosity, a large deviation principle is established by using the weak convergence method skillfully, when the viscosity converges to 0. Due to the appearance of the jumps, it is difficult to close the energy estimates and obtain the desired convergence. Hence, one cannot simply use the weak convergence approach. To overcome the difficulty, one introduces special norms for new arguments and more careful analysis.

Large deviation principles for a 2D stochastic Allen–Cahn–Navier–Stokes driven by jump noise

2021 ◽  
Author(s):  
Theodore Tachim Medjo
Keyword(s):  
Stokes System ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Large Deviation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Deviation Principles ◽  
Convergence Method ◽  
Continuous Time Processes ◽  
Weak Convergence Method

In this paper, we derive a large deviation principle for a stochastic 2D Allen–Cahn–Navier–Stokes system with a multiplicative noise of Lévy type. The model consists of the Navier–Stokes equations for the velocity, coupled with a Allen–Cahn system for the order (phase) parameter. The proof is based on the weak convergence method introduced in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. Henri Poincarà ⓒ Probab. Stat. 47(3) (2011) 725–747].

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