Contents Online
Communications in Mathematical Sciences
Volume 22 (2024)
Number 2
Stability and decay rate of viscous contact wave to one-dimensional compressible Navier-Stokes equations
Pages: 315 – 331
DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n2.a2
Authors
Abstract
This paper studies the large-time asymptotic stability and optimal time-decay rate of viscous contact wave to one-dimensional compressible Navier–Stokes equations. We prove that one-dimensional compressible Navier–Stokes equations are asymptotically stable for viscous contact wave with arbitrarily large strength, under large initial perturbations. The time optimal decay rate of viscous contact wave is also obtained under the small initial perturbations. In the proof, the Lagrange transform is used to cancel the convection terms, which are difficult to estimate due to the lower spatial derivatives compared with the diffusion terms.
Keywords
compressible Navier–Stokes equations, stability, decay rate, viscous contact wave
2010 Mathematics Subject Classification
35Q30, 76N10
Received 15 September 2022
Received revised 15 January 2023
Accepted 19 June 2023
Published 1 February 2024