Knudsen boundary layer equations with incoming boundary condition: full range of cutoff collision kernels and Mach numbers of the far field
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915094408986624 |
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| author | Jiang, Ning Luo, Yi-Long Wu, Yulong Yang, Tong |
| author_facet | Jiang, Ning Luo, Yi-Long Wu, Yulong Yang, Tong |
| contents | This paper establishes tahe existence and uniqueness of the nonlinear Knudsen layer equation with incoming boundary conditions. It is well-known that the solvability conditions of the problem vary with the Mach number of the far Maxwellian $\mathcal{M}^\infty$. We consider full ranges of cutoff collision kernels (i.e., $- 3 < γ\leq 1$) and all the Mach numbers of the far field in the $L^\infty_{x,v}$ framework. Additionally, the solution exhibits exponential decay $\exp \{- c x^\frac{2}{3 - γ} - c |v|^2 \}$ for some $c > 0$. To address the general angular cutoff collision kernel, we introduce a $(x,v)$-mixed weight $σ$. The proof is essentially bsed on adding an artificial damping term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knudsen boundary layer equations with incoming boundary condition: full range of cutoff collision kernels and Mach numbers of the far field Jiang, Ning Luo, Yi-Long Wu, Yulong Yang, Tong Analysis of PDEs 35Q20, 76P05, 35F30, 35B45, 35A01, 35A02 This paper establishes tahe existence and uniqueness of the nonlinear Knudsen layer equation with incoming boundary conditions. It is well-known that the solvability conditions of the problem vary with the Mach number of the far Maxwellian $\mathcal{M}^\infty$. We consider full ranges of cutoff collision kernels (i.e., $- 3 < γ\leq 1$) and all the Mach numbers of the far field in the $L^\infty_{x,v}$ framework. Additionally, the solution exhibits exponential decay $\exp \{- c x^\frac{2}{3 - γ} - c |v|^2 \}$ for some $c > 0$. To address the general angular cutoff collision kernel, we introduce a $(x,v)$-mixed weight $σ$. The proof is essentially bsed on adding an artificial damping term. |
| title | Knudsen boundary layer equations with incoming boundary condition: full range of cutoff collision kernels and Mach numbers of the far field |
| topic | Analysis of PDEs 35Q20, 76P05, 35F30, 35B45, 35A01, 35A02 |
| url | https://arxiv.org/abs/2501.04035 |