Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912018717474816 |
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| author | Liu, Chenguang Xu, Liping Zhang, An |
| author_facet | Liu, Chenguang Xu, Liping Zhang, An |
| contents | In this paper, we prove that the Kac stochastic particle system converges to the weak solution of the spatially homogeneous Boltzmann equation for hard potentials and hard spheres. We give, under the initial data with finite exponential moment assumption, an explicit rate of propagation of chaos in squared Wasserstein distance with quadratic cost by using a double coupling technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials Liu, Chenguang Xu, Liping Zhang, An Probability Mathematical Physics Analysis of PDEs In this paper, we prove that the Kac stochastic particle system converges to the weak solution of the spatially homogeneous Boltzmann equation for hard potentials and hard spheres. We give, under the initial data with finite exponential moment assumption, an explicit rate of propagation of chaos in squared Wasserstein distance with quadratic cost by using a double coupling technique. |
| title | Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2409.04031 |