Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916594979962880 |
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| author | Han, Sungho Kim, Jeongho |
| author_facet | Han, Sungho Kim, Jeongho |
| contents | We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg type, called the Navier-Stokes-Korteweg(NSK) system. Precisely, we show that the solution to the NSK system asymptotically converges to the composition of the rarefaction wave and shifted viscous-dispersive shock wave, under certain smallness assumption on the initial perturbation and strength of the waves. Our method is based on the method of $a$-contraction with shift developed by Kang and Vasseur \cite{KV16}, successfully applied to obtain contraction or stability of nonlinear waves for hyperbolic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type Han, Sungho Kim, Jeongho Analysis of PDEs 35Q35, 76N06 We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg type, called the Navier-Stokes-Korteweg(NSK) system. Precisely, we show that the solution to the NSK system asymptotically converges to the composition of the rarefaction wave and shifted viscous-dispersive shock wave, under certain smallness assumption on the initial perturbation and strength of the waves. Our method is based on the method of $a$-contraction with shift developed by Kang and Vasseur \cite{KV16}, successfully applied to obtain contraction or stability of nonlinear waves for hyperbolic systems. |
| title | Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type |
| topic | Analysis of PDEs 35Q35, 76N06 |
| url | https://arxiv.org/abs/2502.01063 |