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].

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.

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>

Wave propagation for the compressible Navier–Stokes equations

2015 ◽  
Vol 12 (02) ◽  
pp. 385-445 ◽  
Author(s):  
Tai-Ping Liu ◽  
Se Eun Noh
Keyword(s):  
Green Function ◽  
Stokes Equations ◽  
Low Frequency ◽  
Explicit Construction ◽  
Large Time Behavior ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
The Green Function

We establish the pointwise description of solutions to the isentropic Navier–Stokes equations for compressible fluids in three spatial dimensions. First, we give an explicit construction of the Green function for the linearized system. The Green function consists of singular waves, which dominate the short-time behavior, while the low frequency waves, the dissipative Huygens, diffusion and Riesz waves representing the large-time behavior. The nonlinear terms are treated by a suitable combination of energy estimates and pointwise estimates using the Duhamel's principle for the Green function.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

scholarly journals Large deviations for SPDEs of jump type

2015 ◽  
Vol 15 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Xue Yang ◽  
Jianliang Zhai ◽  
Tusheng Zhang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Evolution Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Random Measures ◽  
Convergence Method ◽  
Weak Convergence Method

In this paper, we establish a large deviation principle for a fully nonlinear stochastic evolution equation driven by both Brownian motions and Poisson random measures on a given Hilbert space H. The weak convergence method plays an important role.

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