The half-space problem of evaporation and condensation for polyatomic gases and entropy inequalities
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| Format: | Preprint |
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2025
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| _version_ | 1866912867816570880 |
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| author | Bernhoff, Niclas Brull, Stephane Wadbro, Eddie |
| author_facet | Bernhoff, Niclas Brull, Stephane Wadbro, Eddie |
| contents | This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space are distributed as a Maxwellian, an equilibrium distribution characterized by macroscopic parameters of the boundary. At the far end, the gas tends to an equilibrium distribution, which is also Maxwellian. Using conservation laws and an entropy inequality, we derive relations between the macroscopic parameters of the boundary and at infinity required for the existence of solutions. The relations vary depending on the sign of the Mach number at infinity, which dictates whether evaporation or condensation takes place at the interface between the gas and the condensed phase. We explore the obtained relations numerically. This investigation reveals that, although the relations are qualitatively similar for various internal degrees of freedom of the gas, clear quantitative differences exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The half-space problem of evaporation and condensation for polyatomic gases and entropy inequalities Bernhoff, Niclas Brull, Stephane Wadbro, Eddie Analysis of PDEs Mathematical Physics 82C40, 76P05 This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space are distributed as a Maxwellian, an equilibrium distribution characterized by macroscopic parameters of the boundary. At the far end, the gas tends to an equilibrium distribution, which is also Maxwellian. Using conservation laws and an entropy inequality, we derive relations between the macroscopic parameters of the boundary and at infinity required for the existence of solutions. The relations vary depending on the sign of the Mach number at infinity, which dictates whether evaporation or condensation takes place at the interface between the gas and the condensed phase. We explore the obtained relations numerically. This investigation reveals that, although the relations are qualitatively similar for various internal degrees of freedom of the gas, clear quantitative differences exist. |
| title | The half-space problem of evaporation and condensation for polyatomic gases and entropy inequalities |
| topic | Analysis of PDEs Mathematical Physics 82C40, 76P05 |
| url | https://arxiv.org/abs/2507.01647 |