Time-asymptotic stability of composite wave of viscous shocks and viscous contact wave for Navier-Stokes-Fourier equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910017073971200 |
|---|---|
| author | Huang, Xushan Lee, Hobin |
| author_facet | Huang, Xushan Lee, Hobin |
| contents | We investigate the nonlinear time-asymptotic stability of the composite wave consisting of two viscous shocks and a viscous contact discontinuity for the one-dimensional compressible Navier-Stokes-Fourier (NSF) equations. Specifically, we establish that if the composite wave strength and the perturbations are sufficiently small, the NSF system admits a unique global-in-time strong solution, which converges uniformly in space as time tends to infinity, towards the corresponding composite wave, up to dynamical shifts in the positions of the two viscous shocks. Notably, the strengths of the two viscous shocks can be chosen independently. Our proof relies upon the $a$-contraction method with time-dependent shifts and suitable weight functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-asymptotic stability of composite wave of viscous shocks and viscous contact wave for Navier-Stokes-Fourier equations Huang, Xushan Lee, Hobin Analysis of PDEs 35Q35, 76N06 We investigate the nonlinear time-asymptotic stability of the composite wave consisting of two viscous shocks and a viscous contact discontinuity for the one-dimensional compressible Navier-Stokes-Fourier (NSF) equations. Specifically, we establish that if the composite wave strength and the perturbations are sufficiently small, the NSF system admits a unique global-in-time strong solution, which converges uniformly in space as time tends to infinity, towards the corresponding composite wave, up to dynamical shifts in the positions of the two viscous shocks. Notably, the strengths of the two viscous shocks can be chosen independently. Our proof relies upon the $a$-contraction method with time-dependent shifts and suitable weight functions. |
| title | Time-asymptotic stability of composite wave of viscous shocks and viscous contact wave for Navier-Stokes-Fourier equations |
| topic | Analysis of PDEs 35Q35, 76N06 |
| url | https://arxiv.org/abs/2504.04014 |