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Long-time behavior for 2D non-autonomous g-Navier-Stokes equations

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Anh C., Quyet D.

Annales Polonici Mathematici

2012

tom 103

nr 3

277-302

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 $𝓓_σ$-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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Anh C.

1 Quyet D.

1 2012

Wyniki wyszukiwania

Long-time behavior for 2D non-autonomous g-Navier-Stokes equations