2025/10/20 by Irena Lasiecka, Lasiecka, Irena, Vando Narciso +1
Engineering · Mathematics · #35B33 #35B40 #35B41 #35L05 #35L70 #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2510.18042
openalex publication_date 2025/10/20 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/30
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong monotonicity of the damping at the origin, it is shown that the originally unstable quintic wave is uniformly stabilised to a finite dimensional and smooth set. Moreover, the existence of exponential attractor is established. In order to handle \enquoteenergy criticality of both sources and damping, the methods used depend on enhanced dissipation \citeBociu-lasiecka-jde, energy \it identity for weak solutions \citeKoch-lasiecka, an adaptation of Ball's method \citeball, and the theory of quasi-stable systems \citechueshov-white.