Stability properties of the steady state for the isentropic compressible Navier-Stokes equations with density dependent viscosity in bounded intervals

2019/05/02 by Marta Strani, Strani, Marta
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1905.00770

openalex publication_date 2019/05/02 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We prove existence and asymptotic stability of the stationary solution for the compressible Navier-Stokes equations for isentropic gas dynamics with a density dependent diffusion in a bounded interval. We present the necessary conditions to be imposed on the boundary data which ensure existence and uniqueness of the steady state, and we subsequent investigate its stability properties by means of the construction of a suitable Lyapunov functional for the system. The Saint-Venant system, modeling the dynamics of a shallow compressible fluid, fits into this general framework.

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