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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02531 |
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| _version_ | 1866913827456548864 |
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| author | Li, Hai-Liang Wang, Yuexun Zhang, Yue |
| author_facet | Li, Hai-Liang Wang, Yuexun Zhang, Yue |
| contents | In this paper, we study the well-posedness of classical solutions to a two-phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier-Stokes equations via a drag forcing term. We consider the case that the fluid densities may contain a vacuum, and the viscosities are density-dependent functions. Under suitable assumptions on the initial data, we show that the finite-energy (i.e., in the inhomogeneous Sobolev space) classical solutions to the Cauchy problem of this coupled system do not exist for any small time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-existence of classical solutions to a two-phase flow model with vacuum Li, Hai-Liang Wang, Yuexun Zhang, Yue Analysis of PDEs 35A01, 76N06, 35Q31 In this paper, we study the well-posedness of classical solutions to a two-phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier-Stokes equations via a drag forcing term. We consider the case that the fluid densities may contain a vacuum, and the viscosities are density-dependent functions. Under suitable assumptions on the initial data, we show that the finite-energy (i.e., in the inhomogeneous Sobolev space) classical solutions to the Cauchy problem of this coupled system do not exist for any small time. |
| title | Non-existence of classical solutions to a two-phase flow model with vacuum |
| topic | Analysis of PDEs 35A01, 76N06, 35Q31 |
| url | https://arxiv.org/abs/2402.02531 |