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 REFINED A PRIORI ESTIMATES FOR THE AXISYMMETRIC NAVIER-STOKES EQUATIONS

2017 ◽  
Vol 7 (2) ◽  
pp. 554-558 ◽  
Author(s):  
Zujin Zhang ◽  
◽  
Xiqin Ouyang ◽  
Xian Yang ◽  
◽  
...  
Keyword(s):  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates

scholarly journals Maximum Norm Estimates of the Solution of the Navier-Stokes Equations in the Halfspace with Bounded Initial Data

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Pathak
Keyword(s):  
Initial Data ◽  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Maximum Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Norm Estimates ◽  
Priori Estimates ◽  
The Cauchy Problem

In this paper, I consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝ + n for n ≥ 3 with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a continuation of my work in my previous papers, where the initial data are considered in T n and ℝ n respectively. In this paper, because of the nonempty boundary in our domain of interest, the details in obtaining the desired result are significantly different and more challenging than the work of my previous papers. This challenges arise due to the possible noncommutativity nature of the Leray projector with the derivatives in the direction of normal to the boundary of the domain of interest. Therefore, we only consider one derivative of the velocity field in that direction.

scholarly journals A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations with periodic initial data

2019 ◽  
Vol 36 (1-2) ◽  
pp. 39-50
Author(s):  
Santosh Pathak
Keyword(s):  
Initial Data ◽  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Maximum Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Periodic Initial Data

In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in Rn for n ≥ 3 with smooth periodic initial data and derive a priori estimtes of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a special case of a paper by H-O Kreiss and J. Lorenz which also generalizes the main result of their paper to higher dimension.

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.

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>

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