Hilbert expansion of the Boltzmann equation on a 2-dimensional disk with specular boundary condition
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909586265473024 |
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| author | Huang, Feimin Ouyang, Jing Wang, Yong |
| author_facet | Huang, Feimin Ouyang, Jing Wang, Yong |
| contents | In the present paper, we concern the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition in a two-dimensional disk to the compressible Euler equations. Due to the non-zero curvature and non-zero tangential velocity of compressible Euler solution on the boundary, new difficulties arise in the construction of Knudsen boundary layer. By employing the geometric correction, and an innovative and refined $L^2-L^\infty$ method, we establish the existence and space-decay for a truncated Knudsen boundary layer. Then, by the Hilbert expansion of multi-scales, we successfully justify the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition to the compressible Euler equations in the two-dimensional disk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert expansion of the Boltzmann equation on a 2-dimensional disk with specular boundary condition Huang, Feimin Ouyang, Jing Wang, Yong Analysis of PDEs In the present paper, we concern the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition in a two-dimensional disk to the compressible Euler equations. Due to the non-zero curvature and non-zero tangential velocity of compressible Euler solution on the boundary, new difficulties arise in the construction of Knudsen boundary layer. By employing the geometric correction, and an innovative and refined $L^2-L^\infty$ method, we establish the existence and space-decay for a truncated Knudsen boundary layer. Then, by the Hilbert expansion of multi-scales, we successfully justify the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition to the compressible Euler equations in the two-dimensional disk. |
| title | Hilbert expansion of the Boltzmann equation on a 2-dimensional disk with specular boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.14932 |