On the Existence of Boundary Layer Separation for Incompressible Fluid Flow in the Half-Space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909028452401152 |
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| author | Chang, Tongkeun Kang, Kyungkeun |
| author_facet | Chang, Tongkeun Kang, Kyungkeun |
| contents | We consider the Stokes system in the half-space with localized boundary data. We prove that a boundary layer separation point exists provided that a certain singular integral determined by the boundary data is negative. On the other hand, if this integral is strictly positive, then boundary layer separation does not occur. When boundary layer separation occurs, we also investigate the dynamics of the separation point and the sign of the pressure gradient. Furthermore, by a perturbation argument, we construct solutions to the Navier--Stokes equations in the half-space that exhibit the same qualitative behavior as in the Stokes case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Existence of Boundary Layer Separation for Incompressible Fluid Flow in the Half-Space Chang, Tongkeun Kang, Kyungkeun Analysis of PDEs We consider the Stokes system in the half-space with localized boundary data. We prove that a boundary layer separation point exists provided that a certain singular integral determined by the boundary data is negative. On the other hand, if this integral is strictly positive, then boundary layer separation does not occur. When boundary layer separation occurs, we also investigate the dynamics of the separation point and the sign of the pressure gradient. Furthermore, by a perturbation argument, we construct solutions to the Navier--Stokes equations in the half-space that exhibit the same qualitative behavior as in the Stokes case. |
| title | On the Existence of Boundary Layer Separation for Incompressible Fluid Flow in the Half-Space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.08573 |