Asymptotic behavior of strong solutions to 2D $g$-Navier-Stokes equations
Commun. Korean Math. Soc. 2014 Vol. 29, No. 4, 505-518
https://doi.org/10.4134/CKMS.2014.29.4.505
Printed October 1, 2014
Dao Trong Quyet
Le Quy Don Technical University
Abstract : Considered here is the first initial boundary value problem for the two-dimensional $g$-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.
Keywords : $g$-Navier-Stokes equations, global attractor, stability, stationary solution, long-time finite dimensional approximation
MSC numbers : 35B35, 35B41, 35D35, 35Q35
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