Long-time dynamics for a coupled fluid-thermoelastic plate model with second sound

In this paper, we consider the long time behavior of the coupling problem between the fluid and thermoelastic plate under external forces, while the heat effects are modeled by the Cattaneo law giving rise to a “second sound” effect. By virtue of the semigroup method combined with the boundedness of natural energy, we prove the existence of global solution, through using the polishing technique to realize the zero-average multipliers and the Stokes operator to solve the matching problem of multipliers between fluid and plate equations. We then construct the appropriate Lyapunov functional to obtain asymptotic compactness of the dynamical system and prove the existence of a smooth global attractor.