The fractal dimension of pullback attractors for the 2D Navier–Stokes equations with delay

2020 ◽  
Vol 43 (17) ◽  
pp. 9637-9653
Author(s):  
Xin‐Guang Yang ◽  
Boling Guo ◽  
Chunxiao Guo ◽  
Desheng Li
Keyword(s):  
Fractal Dimension ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Equations With Delay

scholarly journals On the Dimension of the Pullback Attractors for g-Navier-Stokes Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Asymptotic Behaviour ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
Navier Stokes Equations

We consider the asymptotic behaviour of nonautonomous 2D g-Navier-Stokes equations in bounded domainΩ. Assuming thatf∈Lloc2, which is translation bounded, the existence of the pullback attractor is proved inL2(Ω)andH1(Ω). It is proved that the fractal dimension of the pullback attractor is finite.

scholarly journals The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Uniform Attractor ◽  
Navier Stokes Equations ◽  
Finite Dimensional ◽  
Uniform Attractors

We consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain . Assuming , we establish the existence of the uniform attractor in and . The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.

Pullback Attractors for 2D Navier-Stokes Equations with Delays and Their Regularity

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Julia García-Luengo ◽  
Pedro Marín-Rubio ◽  
José Real
Keyword(s):  
Dynamical Systems ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Existence Of Solution ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Delay Function ◽  
Measurability Condition ◽  
Delayed Time

AbstractIn this paper we obtain some results on the existence of solution, and of pullback attractors, for a 2D Navier-Stokes model with finite delay studied in [4] and [6]. Actually, we prove a result of existence and uniqueness of solution under less restrictive assumptions than in [4]. More precisely, we remove a condition on square integrable control of the memory terms, which allows us to consider a bigger class of delay terms (for instance, just under a measurability condition on the delay function leading the delayed time). After that, we deal with dynamical systems in suitable phase spaces within two metrics, the L

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