Pullback attractors for nonautonomous 2D Bénard problem in some unbounded domains (Q2847208)

The authors study the asymptotic behavior of solutions of the system defined in a domain \(D\) in \(\mathbb R^2\): NEWLINE\[NEWLINE u_t + (u \cdot \nabla ) u -\nu \Delta u +\nabla p = f(x,t) + \alpha {\overrightarrow{e_2}}(T-T_0), \quad \nabla \cdot u=0, NEWLINE\]NEWLINE NEWLINE\[NEWLINE T_t + (u\cdot \nabla T) T -\kappa \Delta T =g(x,t), NEWLINE\]NEWLINE where \(\nu\) and \(\kappa\) are positive constants. Under the assumption that the Poincaré inequality holds on \(D\), the authors prove the existence of pullback attractors for the system. The finite dimensionality of the attractor is also established.