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Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

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Anh C., Son D.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

tom 62

nr 3

265-289

We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove 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.

Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains

100%

Anh C., Son D.

Annales Polonici Mathematici

2015

tom 113

nr 2

129-154

We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. 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 pullback $D_σ$-attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Anh C.

2 Son D.

1 2015

1 2014

Wyniki wyszukiwania

Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains