Large Time Behavior and Sharp Interface Limit of Compressible Navier-Stokes/Allen-Cahn System for Interacting Shock Waves
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916273040916480 |
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| author | Chen, Yazhou He, Qiaolin Shi, Xiaoding Wang, Xiaoping |
| author_facet | Chen, Yazhou He, Qiaolin Shi, Xiaoding Wang, Xiaoping |
| contents | In this paper, we study the large time behavior and sharp interface limit of the Cauchy problem for compressible Navier-Stokes/Allen-Cahn system with interaction shock waves in the same family. This system is an important mathematical model for describing the motion of immiscible two-phase flow. The results show that, if the initial density and velocity are near the superposition of two shock waves in the same family, then there exists a unique global solution to the compressible Navier-Stokes/Allen-Cahn system, and this solution asymptotically converges to the superposition of the viscous shock wave and rarefaction wave which moving in opposite directions. Moreover, this global-in-time solution converges to the entropy solution of $p$-system in $L^\infty$-norm as the thickness of the diffusion interface tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Time Behavior and Sharp Interface Limit of Compressible Navier-Stokes/Allen-Cahn System for Interacting Shock Waves Chen, Yazhou He, Qiaolin Shi, Xiaoding Wang, Xiaoping Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 In this paper, we study the large time behavior and sharp interface limit of the Cauchy problem for compressible Navier-Stokes/Allen-Cahn system with interaction shock waves in the same family. This system is an important mathematical model for describing the motion of immiscible two-phase flow. The results show that, if the initial density and velocity are near the superposition of two shock waves in the same family, then there exists a unique global solution to the compressible Navier-Stokes/Allen-Cahn system, and this solution asymptotically converges to the superposition of the viscous shock wave and rarefaction wave which moving in opposite directions. Moreover, this global-in-time solution converges to the entropy solution of $p$-system in $L^\infty$-norm as the thickness of the diffusion interface tends to zero. |
| title | Large Time Behavior and Sharp Interface Limit of Compressible Navier-Stokes/Allen-Cahn System for Interacting Shock Waves |
| topic | Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 |
| url | https://arxiv.org/abs/2406.01902 |