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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.19846 |
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| _version_ | 1866908792206131200 |
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| author | Huang, Qian Rohde, Christian Zhang, Ruixi |
| author_facet | Huang, Qian Rohde, Christian Zhang, Ruixi |
| contents | We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility method. With vanishingly small perturbations of initial velocity, we rigorously prove the simultaneous convergence of fluid velocity and pressure toward the Navier-Stokes limit in the three-dimensional case by constructing an intermediate affine system to obtain the necessary error estimates for the pressure. Furthermore, we extend the velocity convergence analysis to the case of $\mathcal O(1)$ initial velocity perturbations, and establish the global-in-time recovery of the velocity field using a modulated energy structure and delicate bootstrap arguments in both two- and three-dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations Huang, Qian Rohde, Christian Zhang, Ruixi Analysis of PDEs We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility method. With vanishingly small perturbations of initial velocity, we rigorously prove the simultaneous convergence of fluid velocity and pressure toward the Navier-Stokes limit in the three-dimensional case by constructing an intermediate affine system to obtain the necessary error estimates for the pressure. Furthermore, we extend the velocity convergence analysis to the case of $\mathcal O(1)$ initial velocity perturbations, and establish the global-in-time recovery of the velocity field using a modulated energy structure and delicate bootstrap arguments in both two- and three-dimensional settings. |
| title | Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.19846 |