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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.22877 |
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| _version_ | 1866910006096429056 |
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| author | Yuan, Bing Zhang, Rong Zhou, Peng |
| author_facet | Yuan, Bing Zhang, Rong Zhou, Peng |
| contents | This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key estimates of $\|\nabla ρ\|_{L_t^\infty L_x^q},q>2$ without any smallness asuumption on the initial data, and thus establish the global existence of the strong solutions with the far-field density being either vacuum or nonvacuum. Notably, the initial data can be arbitrarily large and the initial density is allowed to vanish. Furthermore, the large-time asymptotic behavior of the gradients of the velocity and the pressure is also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Well-posedness of Strong Solutions to the Cauchy Problem of 2D Nonhomogeneous Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum Yuan, Bing Zhang, Rong Zhou, Peng Analysis of PDEs This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key estimates of $\|\nabla ρ\|_{L_t^\infty L_x^q},q>2$ without any smallness asuumption on the initial data, and thus establish the global existence of the strong solutions with the far-field density being either vacuum or nonvacuum. Notably, the initial data can be arbitrarily large and the initial density is allowed to vanish. Furthermore, the large-time asymptotic behavior of the gradients of the velocity and the pressure is also established. |
| title | Global Well-posedness of Strong Solutions to the Cauchy Problem of 2D Nonhomogeneous Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.22877 |