Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909270911483904 |
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| author | Chen, Xuwen Holmer, Justin |
| author_facet | Chen, Xuwen Holmer, Justin |
| contents | We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium nor self-similar, to the equation, and prove that the well/ill-posedness threshold in $H^{s}$ Sobolev space is exactly at regularity $s=1$, despite the fact that the equation is scale invariant at $s=\frac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11931 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel Chen, Xuwen Holmer, Justin Analysis of PDEs Mathematical Physics We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium nor self-similar, to the equation, and prove that the well/ill-posedness threshold in $H^{s}$ Sobolev space is exactly at regularity $s=1$, despite the fact that the equation is scale invariant at $s=\frac{1}{2}$. |
| title | Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2206.11931 |