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

• Autorzy: Cung The Anh , Dao Trong Quyet
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37L30: Attractors and their dimensions, Lyapunov exponents
• 35Q30: Navier-Stokes equations
• 35B41: Attractors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 3
• Strony: 277-302

Daty

wydano

2012

Twórcy

autor

Cung The Anh

• Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

autor

Dao Trong Quyet

• Faculty of Information Technology, Le Qui Don Technical University, 100 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

Identyfikatory

DOI

10.4064/ap103-3-5