scholarly journals Global attractor for the Navier–Stokes equations with fractional deconvolution

2014 ◽  
Vol 22 (4) ◽  
pp. 811-848 ◽  
Author(s):  
Davide Catania ◽  
Alessandro Morando ◽  
Paola Trebeschi
Keyword(s):  
Global Attractor ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

ATTRACTORS AND NEO-ATTRACTORS FOR 3D STOCHASTIC NAVIER–STOKES EQUATIONS

2005 ◽  
Vol 05 (04) ◽  
pp. 487-533 ◽  
Author(s):  
NIGEL J. CUTLAND ◽  
H. JEROME KEISLER
Keyword(s):  
Global Attractor ◽  
Ad Hoc ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Nonstandard Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loeb Space

In [14] nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell's approach [26]. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor — a notion introduced here that arises naturally from the Keisler–Fajardo theory of neometric spaces [18]. To set this result in context we first survey the use of Loeb space and nonstandard techniques in the study of attractors, with special emphasis on results obtained for the Navier–Stokes equations both deterministic and stochastic, showing that such methods are well-suited to this enterprise.

EXISTENCE OF A GLOBAL ATTRACTOR FOR THE SLIGHTLY COMPRESSIBLE 2-D NAVIER–STOKES EQUATIONS IN THE CASE OF A THERMOHYDRAULIC PROBLEM

1996 ◽  
Vol 06 (01) ◽  
pp. 59-75 ◽  
Author(s):  
SERGE NJAMKEPO
Keyword(s):  
Global Attractor ◽  
Compressible Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slightly Compressible

A theorem by J. M. Ghidaglia and R. Temam shows the existence and finitness of attractors for 2-D Navier–Stokes equations for a sligthly compressible fluid. In this paper we extend their result to the equations of thermohydraulic for the same fluid.

scholarly journals On whether zero is in the global attractor of the 2D Navier–Stokes equations

Nonlinearity ◽  
2014 ◽  
Vol 27 (11) ◽  
pp. 2755-2770 ◽  
Author(s):  
Ciprian Foias ◽  
Michael S Jolly ◽  
Yong Yang ◽  
Bingsheng Zhang
Keyword(s):  
Global Attractor ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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