Asymptotically Autonomous Robustness of Pullback Attractors for Non-autonomous Newton-Boussinesq Equation on Unbounded Poincaré Domains

Abstract

This paper studies the asymptotic behavior of solutions to the non-autonomous Newton-Boussinesq equation defined on a two-dimensional unbounded Poincaré domain. Based on the well-posedness of solutions in \(L^{2}(\mathcal{O}) \times L^{2}(\mathcal{O})\), we construct a continuous non-autonomous dynamical system in this space and prove the existence of a unique tempered pullback attractor. Moreover, under the assumption that the time-dependent external forces converge to time-independent fnctions as time approaches positive or negative infinity, we establish the asymptotically autonomous upper semicontinuity of the attractors. The main difficulty arising from the lack of compact Sobolev embeddings on unbounded domains is overcome by deriving uniform tail estimates for the solutions.