Phase Transition in Non-isentropic Compressible Immiscible Two-Phase Flow with van der Waals Equation of State
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| Format: | Preprint |
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2025
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| _version_ | 1866908422532759552 |
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| author | Chen, Yazhou Peng, Yi Shi, Xiaoding Wang, Xiaoping |
| author_facet | Chen, Yazhou Peng, Yi Shi, Xiaoding Wang, Xiaoping |
| contents | This study establishes the global well-posedness of the compressible non-isentropic Navier-Stokes/Allen-Cahn system governed by the van der Waals equation of state $p(ρ,θ)=- aρ^2+\frac{Rθρ}{1-bρ}$ and degenerate thermal conductivity $κ(θ)=\tildeκθ^β$, where $p$, $ρ$ and $θ$ are the pressure, the density and the temperature of the flow respectively, and $a,b,R,\tildeκ$ are positive constants related to the physical properties of the flow. Navier-Stokes/Allen-Cahn system models immiscible two-phase flow with diffusive interfaces, where the non-monotonic pressure-density relationship in the van der Waals equation drives gas-liquid phase transitions. By developing a refined $L^2$-energy framework, we prove the existence and uniqueness of global strong solutions to the one-dimensional Cauchy problem for non-vacuum and finite-temperature initial data, without imposing smallness restrictions on the initial conditions. The findings demonstrate that despite non-monotonic pressure inducing substantial density fluctuations and triggering phase transitions, all physical quantities remain bounded over finite time intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase Transition in Non-isentropic Compressible Immiscible Two-Phase Flow with van der Waals Equation of State Chen, Yazhou Peng, Yi Shi, Xiaoding Wang, Xiaoping Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 This study establishes the global well-posedness of the compressible non-isentropic Navier-Stokes/Allen-Cahn system governed by the van der Waals equation of state $p(ρ,θ)=- aρ^2+\frac{Rθρ}{1-bρ}$ and degenerate thermal conductivity $κ(θ)=\tildeκθ^β$, where $p$, $ρ$ and $θ$ are the pressure, the density and the temperature of the flow respectively, and $a,b,R,\tildeκ$ are positive constants related to the physical properties of the flow. Navier-Stokes/Allen-Cahn system models immiscible two-phase flow with diffusive interfaces, where the non-monotonic pressure-density relationship in the van der Waals equation drives gas-liquid phase transitions. By developing a refined $L^2$-energy framework, we prove the existence and uniqueness of global strong solutions to the one-dimensional Cauchy problem for non-vacuum and finite-temperature initial data, without imposing smallness restrictions on the initial conditions. The findings demonstrate that despite non-monotonic pressure inducing substantial density fluctuations and triggering phase transitions, all physical quantities remain bounded over finite time intervals. |
| title | Phase Transition in Non-isentropic Compressible Immiscible Two-Phase Flow with van der Waals Equation of State |
| topic | Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 |
| url | https://arxiv.org/abs/2506.20955 |