Global well-posedness of 3D two-fluid type model with vacuum: smallness on scaling invariant quantity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914277856641024 |
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| author | Wen, Huanyao Xie, Chanxin |
| author_facet | Wen, Huanyao Xie, Chanxin |
| contents | This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility constraint, and that the newly introduced scaling-invariant initial quantities $\bar P^{\frac{ 3}γ} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right) \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ and $\bar P^{\frac{6}γ+1} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right)^3 \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ are sufficiently small, the global well-posedness of strong solutions to the two-fluid type model is derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of 3D two-fluid type model with vacuum: smallness on scaling invariant quantity Wen, Huanyao Xie, Chanxin Analysis of PDEs This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility constraint, and that the newly introduced scaling-invariant initial quantities $\bar P^{\frac{ 3}γ} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right) \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ and $\bar P^{\frac{6}γ+1} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right)^3 \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ are sufficiently small, the global well-posedness of strong solutions to the two-fluid type model is derived. |
| title | Global well-posedness of 3D two-fluid type model with vacuum: smallness on scaling invariant quantity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.17709 |