2021/12/26 by Zhilei Liang, Liang, Zhilei
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2112.13406
openalex publication_date 2021/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly positive from below and above after a finite period of time. Moreover, higher velocity regularity is obtained via a parabolic type iteration technique. Since then the weak solution conserves its energy equality, and decays exponentially to the equilibrium in L2-norm as time goes to infinity. In addition, assume that the initial momentum is zero, the exponential decay rate is derived for the derivative functions, and the weak solution becomes a strong one in two dimensional space.