Geodesic
Long-time behavior for 2D non-autonomous $g$-Navier–Stokes equations
Cung The Anh1 ; Dao Trong Quyet2
1 Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
2 Faculty of Information Technology Le Qui Don Technical University 100 Hoang Quoc Viet, Cau Giay Hanoi, Vietnam
Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 277-302 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the first initial boundary value problem for the 2D non-autonomous $g$-Navier–Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback $\mathcal D_\sigma$-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent and “small”, the existence, uniqueness and global stability of a stationary solution are also studied.
DOI : 10.4064/ap103-3-5
Keywords: study first initial boundary value problem non autonomous g navier stokes equations arbitrary bounded unbounded domain satisfying poincar inequality existence weak solution problem proved using galerkin method existence unique minimal finite dimensional pullback mathcal sigma attractor process associated problem respect large class non autonomous forcing terms furthermore force time independent small existence uniqueness global stability stationary solution studied

Cung The Anh 1 ; Dao Trong Quyet 2

1 Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
2 Faculty of Information Technology Le Qui Don Technical University 100 Hoang Quoc Viet, Cau Giay Hanoi, Vietnam 
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Cung The Anh; Dao Trong Quyet. Long-time behavior for 2D non-autonomous $g$-Navier–Stokes equations. Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 277-302. doi: 10.4064/ap103-3-5

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