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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.21646 |
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| _version_ | 1866917357806419968 |
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| author | Wang, Gaofeng Wu, Tianfang Xiong, Linjie |
| author_facet | Wang, Gaofeng Wu, Tianfang Xiong, Linjie |
| contents | In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $γ\in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are different which derives to the loss of symmetry to the linearized collision operator. %This paper resolves it precisely by using a framework based on vector-valued functions. We construct the hydrodynamic limit for two species based on the Hilbert expansion method when the Knudsen number is small. The key observation is the precise properties of the linearized collision operators, including the extra operators due to the different particle masses $(m^A \neq m^B)$. In additional, the acoustic limit of the Boltzmann equations for gas mixtures is rigorously justified by assuming the strength of the initial data depends on the Knudsen number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Acoustic limit of Boltzmann equations for gas mixture Wang, Gaofeng Wu, Tianfang Xiong, Linjie Analysis of PDEs 35B38, 35J47 In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $γ\in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are different which derives to the loss of symmetry to the linearized collision operator. %This paper resolves it precisely by using a framework based on vector-valued functions. We construct the hydrodynamic limit for two species based on the Hilbert expansion method when the Knudsen number is small. The key observation is the precise properties of the linearized collision operators, including the extra operators due to the different particle masses $(m^A \neq m^B)$. In additional, the acoustic limit of the Boltzmann equations for gas mixtures is rigorously justified by assuming the strength of the initial data depends on the Knudsen number. |
| title | Acoustic limit of Boltzmann equations for gas mixture |
| topic | Analysis of PDEs 35B38, 35J47 |
| url | https://arxiv.org/abs/2603.21646 |