Asymptotic approximation of a modified compressible Navier-Stokes system
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909628522037248 |
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| author | Goh, Ryan Wayne, C. Eugene Welter, Roland |
| author_facet | Goh, Ryan Wayne, C. Eugene Welter, Roland |
| contents | We study the long time asymptotics of a modified compressible Navier-Stokes system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a new decomposition of the momentum field into its irrotational and incompressible parts, and a new method for approximating solutions of the heat equation in terms of Hermite functions in which $n^{th}$ order approximations can be computed for solutions with $n^{th}$ order moments. We then obtain existence of solutions to the mcNS system and show that the approximation in terms of Hermite functions gives the leading order terms in the long-time asymptotics, and under certain assumptions can be evaluated explicitly. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_12966 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Asymptotic approximation of a modified compressible Navier-Stokes system Goh, Ryan Wayne, C. Eugene Welter, Roland Analysis of PDEs Mathematical Physics Dynamical Systems 76N10 We study the long time asymptotics of a modified compressible Navier-Stokes system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a new decomposition of the momentum field into its irrotational and incompressible parts, and a new method for approximating solutions of the heat equation in terms of Hermite functions in which $n^{th}$ order approximations can be computed for solutions with $n^{th}$ order moments. We then obtain existence of solutions to the mcNS system and show that the approximation in terms of Hermite functions gives the leading order terms in the long-time asymptotics, and under certain assumptions can be evaluated explicitly. |
| title | Asymptotic approximation of a modified compressible Navier-Stokes system |
| topic | Analysis of PDEs Mathematical Physics Dynamical Systems 76N10 |
| url | https://arxiv.org/abs/2012.12966 |