Effect of weak elasticity on Kelvin-Helmholtz instability
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910622223958016 |
|---|---|
| author | Xie, Binqiang Guo, Boling Zhao, Bin |
| author_facet | Xie, Binqiang Guo, Boling Zhao, Bin |
| contents | In this paper, we present an analysis of the Kelvin-Helmholtz instability in two-dimensional ideal compressible elastic flows, providing a rigorous confirmation that weak elasticity has a destabilizing effect on the Kelvin-Helmholtz instability. There are two critical velocities, $U_{\text{low}}$ and $U_{\text{upp}}$, where $U_{\text{low}}$ and $U_{\text{upp}}$ represent the lower and upper critical velocities, respectively. We demonstrate that when the magnitude of the rectilinear solutions satisfies $U_{\text{low}}+cε_{0}\le |\dot{v}^{+}_{1}| \le U_{\text{upp}}-cε_{0}$, the linear and nonlinear ill-posedness of the piecewise smooth solutions of the Kelvin-Helmholtz problem for two-dimensional ideal compressible elastic fluids is established uniformly, where $c$ is the sound speed and $ε_{0}$ is some small enough positive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effect of weak elasticity on Kelvin-Helmholtz instability Xie, Binqiang Guo, Boling Zhao, Bin Analysis of PDEs 35Q35, 35D35 In this paper, we present an analysis of the Kelvin-Helmholtz instability in two-dimensional ideal compressible elastic flows, providing a rigorous confirmation that weak elasticity has a destabilizing effect on the Kelvin-Helmholtz instability. There are two critical velocities, $U_{\text{low}}$ and $U_{\text{upp}}$, where $U_{\text{low}}$ and $U_{\text{upp}}$ represent the lower and upper critical velocities, respectively. We demonstrate that when the magnitude of the rectilinear solutions satisfies $U_{\text{low}}+cε_{0}\le |\dot{v}^{+}_{1}| \le U_{\text{upp}}-cε_{0}$, the linear and nonlinear ill-posedness of the piecewise smooth solutions of the Kelvin-Helmholtz problem for two-dimensional ideal compressible elastic fluids is established uniformly, where $c$ is the sound speed and $ε_{0}$ is some small enough positive constant. |
| title | Effect of weak elasticity on Kelvin-Helmholtz instability |
| topic | Analysis of PDEs 35Q35, 35D35 |
| url | https://arxiv.org/abs/2408.00053 |