Stability of the Favorable Falkner-Skan Profiles for the Stationary Prandtl Equations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916157062119424 |
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| author | Iyer, Sameer |
| author_facet | Iyer, Sameer |
| contents | The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($β\in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $β\fracπ{2}$. The most famous member of this family is the endpoint Blasius profile, $β= 0$, which exhibits pressureless flow over a flat plate. In contrast, the $β> 0$ profiles are physically expected to exhibit a \textit{favorable pressure gradient}, a common adage in the physics literature. In this work, we prove quantitative scattering estimates as $x \rightarrow \infty$ which precisely captures the effect of this favorable gradient through the presence of new ``CK" (Cauchy-Kovalevskaya) terms that appear in a quasilinear energy cascade. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the Favorable Falkner-Skan Profiles for the Stationary Prandtl Equations Iyer, Sameer Analysis of PDEs The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($β\in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $β\fracπ{2}$. The most famous member of this family is the endpoint Blasius profile, $β= 0$, which exhibits pressureless flow over a flat plate. In contrast, the $β> 0$ profiles are physically expected to exhibit a \textit{favorable pressure gradient}, a common adage in the physics literature. In this work, we prove quantitative scattering estimates as $x \rightarrow \infty$ which precisely captures the effect of this favorable gradient through the presence of new ``CK" (Cauchy-Kovalevskaya) terms that appear in a quasilinear energy cascade. |
| title | Stability of the Favorable Falkner-Skan Profiles for the Stationary Prandtl Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.07791 |