Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913461971189760 |
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| author | Chen, Jiajie |
| author_facet | Chen, Jiajie |
| contents | We prove finite-time vorticity blowup in the compressible Euler equations in $\mathbb{R}^d$ for any $d \geq 3$, starting from smooth, localized, and non-vacuous initial data. This is achieved by lifting the vorticity blowup result from [CCSV24] in $\mathbb{R}^2$ to $\mathbb{R}^d$ and utilizing the axisymmetry in $\mathbb{R}^d$. At the time of the first singularity, both vorticity blowup and implosion occur on a sphere $S^{d-2}$. Additionally, the solution exhibits a non-radial implosion, accompanied by a stable swirl velocity that is sufficiently strong to initially dominate the non-radial components and to generate the vorticity blowup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$ Chen, Jiajie Analysis of PDEs Fluid Dynamics We prove finite-time vorticity blowup in the compressible Euler equations in $\mathbb{R}^d$ for any $d \geq 3$, starting from smooth, localized, and non-vacuous initial data. This is achieved by lifting the vorticity blowup result from [CCSV24] in $\mathbb{R}^2$ to $\mathbb{R}^d$ and utilizing the axisymmetry in $\mathbb{R}^d$. At the time of the first singularity, both vorticity blowup and implosion occur on a sphere $S^{d-2}$. Additionally, the solution exhibits a non-radial implosion, accompanied by a stable swirl velocity that is sufficiently strong to initially dominate the non-radial components and to generate the vorticity blowup. |
| title | Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$ |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2408.04319 |