Time-velocity decay of solutions to the non-cutoff Boltzmann equation in the whole space
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916226075197440 |
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| author | Cao, Chuqi Duan, Renjun Li, Zongguang |
| author_facet | Cao, Chuqi Duan, Renjun Li, Zongguang |
| contents | In this paper, we consider the perturbed solutions with polynomial tail in large velocities for the non-cutoff Boltzmann equation near global Maxwellians in the whole space. The global in time existence is proved in the weighted Sobolev spaces and the almost optimal time decay is obtained in Fourier transform based low-regularity spaces. The result shows a time-velocity decay structure of solutions that can be decomposed into two parts. One part allows the slow polynomial tail in large velocities, carries the initial data and enjoys the exponential or arbitrarily large polynomial time decay. The other part, with zero initial data, is dominated by the non-negative definite symmetric dissipation and has the exponential velocity decay but only the slow polynomial time decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-velocity decay of solutions to the non-cutoff Boltzmann equation in the whole space Cao, Chuqi Duan, Renjun Li, Zongguang Analysis of PDEs In this paper, we consider the perturbed solutions with polynomial tail in large velocities for the non-cutoff Boltzmann equation near global Maxwellians in the whole space. The global in time existence is proved in the weighted Sobolev spaces and the almost optimal time decay is obtained in Fourier transform based low-regularity spaces. The result shows a time-velocity decay structure of solutions that can be decomposed into two parts. One part allows the slow polynomial tail in large velocities, carries the initial data and enjoys the exponential or arbitrarily large polynomial time decay. The other part, with zero initial data, is dominated by the non-negative definite symmetric dissipation and has the exponential velocity decay but only the slow polynomial time decay. |
| title | Time-velocity decay of solutions to the non-cutoff Boltzmann equation in the whole space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.02804 |