REMOVED: Attractors of non-autonomous 2D Navier–Stokes equations with P-normal external forces

2006 ◽  
Author(s):  
Haitao Song ◽  
Chengkui Zhong
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
External Forces

scholarly journals Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hicham Mahdioui ◽  
Sultana Ben Aadi ◽  
Khalid Akhlil
Keyword(s):  
Stokes Equations ◽  
Dynamic Pressure ◽  
Normal Component ◽  
Galerkin Approximation ◽  
Stability Result ◽  
Clarke Subdifferential ◽  
Navier Stokes ◽  
Directional Growth ◽  
Navier Stokes Equations ◽  
External Forces

In this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under the Rauch condition, we use the Galerkin approximation method and a weak precompactness criterion to ensure the convergence to a desired solution. Moreover, a control problem associated with such system of equations is studied with the help of a stability result with respect to the external forces. At the end of this paper, a more general condition due to Z. Naniewicz, namely the directional growth condition, is considered and all the results are reexamined.

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>

Asymptotic behavior for the Navier–Stokes equations with nonzero external forces

2009 ◽  
Vol 71 (12) ◽  
pp. e292-e302 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Lorenzo Brandolese ◽  
Bum Ja Jin
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
External Forces

scholarly journals CONVERGENCE RATE FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH EXTERNAL FORCE

2006 ◽  
Vol 03 (03) ◽  
pp. 561-574 ◽  
Author(s):  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Convergence Rate ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Optimal Convergence Rate ◽  
Potential Force ◽  
Stationary Potential ◽  
Navier Stokes Equations ◽  
The Stability ◽  
External Forces

For the compressible Navier–Stokes equations with a stationary potential force, the stability of the stationary solutions was studied by Matsumura and Nishida. The convergence rate to the stationary solutions in time was later studied by Deckelnick which was improved by Shibata and Tanaka for more general external forces. This paper deals with the case for the stationary potential force under some smallness condition, to establish an almost optimal convergence rate in L2(ℝN)-norm for N ≥ 3.

Sign in / Sign up

Export Citation Format

Share Document