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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09333 |
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| _version_ | 1866909801332604928 |
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| author | Gancedo, Francisco García-Juárez, Eduardo Luna-Velasco, Paula |
| author_facet | Gancedo, Francisco García-Juárez, Eduardo Luna-Velasco, Paula |
| contents | This paper is concerned with the evolution of two incompressible, immiscible fluids in two dimensions governed by the inhomogeneous Navier-Stokes equations. We prove global-in-time well-posedness, establishing the preservation of the natural $C^{1+γ}$ Hölder regularity of the free boundary, for $0<γ<1$. This is the first result that allows for nonnegative density driven by a low-regularity initial velocity, while also remaining valid in the presence of a small viscosity jump. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast Gancedo, Francisco García-Juárez, Eduardo Luna-Velasco, Paula Analysis of PDEs This paper is concerned with the evolution of two incompressible, immiscible fluids in two dimensions governed by the inhomogeneous Navier-Stokes equations. We prove global-in-time well-posedness, establishing the preservation of the natural $C^{1+γ}$ Hölder regularity of the free boundary, for $0<γ<1$. This is the first result that allows for nonnegative density driven by a low-regularity initial velocity, while also remaining valid in the presence of a small viscosity jump. |
| title | On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.09333 |