Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14696 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917492984643584 |
|---|---|
| author | Jia, Jin Luo, Tao |
| author_facet | Jia, Jin Luo, Tao |
| contents | For 2D compressible Euler equations of isentropic gas, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as shock waves or vortex sheets), by deriving simultaneous energy estimates for acoustic and vorticity waves within the rarefaction wave region \emph{without loss of derivatives} and examinations of the nonlinear superpositions of rarefaction waves with other waves such as shock waves or vortex sheets. The nonlinear superpositions of \emph{shock wave-rarefaction wave} and \emph{rarefaction wave-vortex sheet-rarefaction wave} are achieved by reducing the problems in corner regions to the Cauchy problems with the data prescribed on the plane $Σ_0=\{(t, x_1, x_2): t=0, (x_1, x_2)\in \mathbb{R}\times\mathbb{R}/2π\mathbb{Z}\}$ with discontinuities at $\mathbf{S}_*:=\{(t,x_{1},x_{2})\mid t=0,\ x_{1}=0, x_2\in\mathbb{R}/2π\mathbb{Z} \}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14696 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Dimensional Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics Jia, Jin Luo, Tao Analysis of PDEs For 2D compressible Euler equations of isentropic gas, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as shock waves or vortex sheets), by deriving simultaneous energy estimates for acoustic and vorticity waves within the rarefaction wave region \emph{without loss of derivatives} and examinations of the nonlinear superpositions of rarefaction waves with other waves such as shock waves or vortex sheets. The nonlinear superpositions of \emph{shock wave-rarefaction wave} and \emph{rarefaction wave-vortex sheet-rarefaction wave} are achieved by reducing the problems in corner regions to the Cauchy problems with the data prescribed on the plane $Σ_0=\{(t, x_1, x_2): t=0, (x_1, x_2)\in \mathbb{R}\times\mathbb{R}/2π\mathbb{Z}\}$ with discontinuities at $\mathbf{S}_*:=\{(t,x_{1},x_{2})\mid t=0,\ x_{1}=0, x_2\in\mathbb{R}/2π\mathbb{Z} \}$. |
| title | Multi-Dimensional Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.14696 |