Long time behavior for partly dissipative equations: the slightly compressible 2D-Navier–Stokes equations

1988 ◽  
Vol 1 (1) ◽  
pp. 23-49 ◽  
Author(s):  
J.M. Ghidaglia ◽  
R. Temam
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Navier Stokes Equations ◽  
Slightly Compressible ◽  
Long Time

scholarly journals Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xin-Guang Yang ◽  
Jun-Tao Li
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Navier Stokes Equations ◽  
Upper Semicontinuous ◽  
Long Time ◽  
Linear Damping ◽  
Uniform Attractors

Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

scholarly journals Existence and long-time behavior of solutions to the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

2021 ◽  
Author(s):  
Nguyen Toan
Keyword(s):  
Stokes Equations ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Voigt Model ◽  
Initial Boundary Value

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term $f \in L^2_b(\mathbb{R}; H^{-1}(\Omega))$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.

scholarly journals Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory

2021 ◽  
Author(s):  
Yasi Zheng ◽  
Wenjun Liu ◽  
Yadong Liu
Keyword(s):  
Stokes Equations ◽  
Infinite Delay ◽  
Navier Stokes ◽  
Time Behavior ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Bounded Absorbing Set ◽  
Long Time ◽  
The One ◽  
Class Of Functions

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

scholarly journals Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory

2019 ◽  
Author(s):  
Yasi Zheng ◽  
Wenjun Liu ◽  
Yadong Liu
Keyword(s):  
Stokes Equations ◽  
Infinite Delay ◽  
Navier Stokes ◽  
Time Behavior ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Bounded Absorbing Set ◽  
Long Time ◽  
The One ◽  
Class Of Functions

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

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.

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