Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian

RESUMO

Focusing on the pullback asymptotic behavior exhibited by the system, this paper studies the three-dimensional (3D) non-autonomous Boussinesq equations with fractional Laplacian. For $ \alpha > \frac{5}{4} $ and $ \beta > \frac{5}{8} $, by adopting the $ \ell $-trajectory method introduced in \cite{MP2002}, we demonstrate the existence of both a finite-dimensional pullback attractor and a pullback exponential attractor for the process $ \{L(t, \tau)\}_{t \geq \tau} $ that corresponds to \cref{eq0101} in the phase space $ X_{\ell} $. Furthermore, we establish the existence of a pullback exponential attractor for the process $ \{U(t, \tau)\}_{t \geq \tau} $ within the original phase space $ H_\sigma^\alpha(\Omega) \times H^{\beta}(\Omega) $.