Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary
Feimin Huang, Xiaoding Shi, Yi Wang
TL;DR
This paper proves the asymptotic stability of viscous shock waves in a free boundary setting for one-dimensional compressible Navier-Stokes equations using elementary energy estimates.
Contribution
It establishes the stability of viscous shock waves in a free boundary context, which is a novel extension of prior stability analyses.
Findings
Viscous shock waves are asymptotically stable under smallness conditions.
Elementary energy estimates suffice to prove stability.
The results apply to one-dimensional compressible Navier-Stokes with free boundary.
Abstract
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary energy estimate.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNavier-Stokes equation solutions · Advanced Mathematical Physics Problems · Computational Fluid Dynamics and Aerodynamics