2026/07/27 by Juan Yu, Feng Zhou, Qingru Sun +1
paper · doi:10.1063/5.0333022
This work studies the long-time dynamics of a Lamé system with supercritical and super-supercritical nonlinearities g and f. A key analytical challenge arises from the interplay between the gradient-divergence term (μ + λ)∇ div u and the nonlinearities, especially due to the super-supercritical growth of both f and g. To address this, we combine evolutionary systems theory with energy methods and the quasi-stability approach. Our main results establish the existence and structure of a compact global attractor, and in the supercritical case, we further construct an exponential attractor. These results yield a comprehensive characterization of the asymptotic behavior of the Lamé system.