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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08670 |
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| _version_ | 1866914866588024832 |
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| author | Gualdani, Maria Pia Winter, Raphael |
| author_facet | Gualdani, Maria Pia Winter, Raphael |
| contents | We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian function. We establish global well-posedness and show that the initial bump region will disappear in a time of order one. We prove that the function remains close to an explicit function during the blow-down. As a consequence, our result shows exponential decay in time of the solution towards equilibrium. The key ingredients of our proof are the explicit blow-down function and a novel two-scale linearization in appropriate time-dependent spaces that yields uniform estimates in the perturbation parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A blow-down mechanism for the Landau-Coulomb equation Gualdani, Maria Pia Winter, Raphael Analysis of PDEs Mathematical Physics 35B25 We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian function. We establish global well-posedness and show that the initial bump region will disappear in a time of order one. We prove that the function remains close to an explicit function during the blow-down. As a consequence, our result shows exponential decay in time of the solution towards equilibrium. The key ingredients of our proof are the explicit blow-down function and a novel two-scale linearization in appropriate time-dependent spaces that yields uniform estimates in the perturbation parameter. |
| title | A blow-down mechanism for the Landau-Coulomb equation |
| topic | Analysis of PDEs Mathematical Physics 35B25 |
| url | https://arxiv.org/abs/2407.08670 |