Relative entropy and slightly compressible Navier-Stokes dynamics of the Boltzmann equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908820299579392 |
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| author | Chen, Yuhan Jiang, Ning |
| author_facet | Chen, Yuhan Jiang, Ning |
| contents | This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$,
using the relative entropy method originated from Bardos, Golse, Levermore [{\em Comm. Pure Appl. Math.} {\bf 46} (1993) 667--753] and Yau [{\em Lett. Math. Phys.} {\bf 22} (1991) 63--80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07957 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relative entropy and slightly compressible Navier-Stokes dynamics of the Boltzmann equation Chen, Yuhan Jiang, Ning Analysis of PDEs This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$, using the relative entropy method originated from Bardos, Golse, Levermore [{\em Comm. Pure Appl. Math.} {\bf 46} (1993) 667--753] and Yau [{\em Lett. Math. Phys.} {\bf 22} (1991) 63--80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system. |
| title | Relative entropy and slightly compressible Navier-Stokes dynamics of the Boltzmann equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.07957 |