On existence of weak solutions to a Baer-Nunziato type system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911169939243008 |
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| author | Kalousek, Martin Nečasová, Šárka |
| author_facet | Kalousek, Martin Nečasová, Šárka |
| contents | In this paper, a dissipative version of a compressible one velocity Baer--Nunziato type system for a mixture of two compressible heat conducting gases is considered. The complete existence proof for weak solutions to this system was addressed as an open problem in [6, Section 5]. The purpose of this paper is to prove the global in time existence of weak solutions to the one velocity Baer--Nunziato type system for arbitrary large initial data. The goal is achieved in three steps. Firstly, the given system is transformed into a new one which possesses the "Navier-Stokes-Fourier" structure. Secondly, the new system is solved by an adaptation of the Feireisl--Lions approach for solving the compressible Navier--Stokes equations. Eventually, the existence of a weak solution to the original one velocity Baer--Nunziato system using the almost uniqueness property of renormalized solutions to pure transport equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On existence of weak solutions to a Baer-Nunziato type system Kalousek, Martin Nečasová, Šárka Analysis of PDEs In this paper, a dissipative version of a compressible one velocity Baer--Nunziato type system for a mixture of two compressible heat conducting gases is considered. The complete existence proof for weak solutions to this system was addressed as an open problem in [6, Section 5]. The purpose of this paper is to prove the global in time existence of weak solutions to the one velocity Baer--Nunziato type system for arbitrary large initial data. The goal is achieved in three steps. Firstly, the given system is transformed into a new one which possesses the "Navier-Stokes-Fourier" structure. Secondly, the new system is solved by an adaptation of the Feireisl--Lions approach for solving the compressible Navier--Stokes equations. Eventually, the existence of a weak solution to the original one velocity Baer--Nunziato system using the almost uniqueness property of renormalized solutions to pure transport equations. |
| title | On existence of weak solutions to a Baer-Nunziato type system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.08383 |