2025/06/30 by Lingping Kang, Kang, Lingping, Yanfang Peng +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2506.23807
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the large-time behavior for the barotropic compressible Navier-Stokes equations with large external force in 3D bounded domain. By constructing a suitable Lyapunov functional and using the extra integrability of the density, we state the exponentially decay-in-time to the equilibrium state for Lions-Feireisl's finite-energy weak solutions. In addition, some careful discussion on Taylor expansion also plays a crucial role in our analysis. The main difficulty lies in the fact that the equilibrium state of density is not a constant anymore induced by the large external force. It should be noted that our result can be regarded as an extension of \citePSW to large potential forces case.