Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917571965485056 |
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| author | Li, Wei-Xi Yang, Tong Zhang, Ping |
| author_facet | Li, Wei-Xi Yang, Tong Zhang, Ping |
| contents | We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class $\frac 32$ in the tangential variable and is analytic in the normal variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations Li, Wei-Xi Yang, Tong Zhang, Ping Analysis of PDEs We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class $\frac 32$ in the tangential variable and is analytic in the normal variable. |
| title | Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.11230 |