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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2203.10860 |
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| _version_ | 1866929327630712832 |
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| author | Meyer, David Seis, Christian |
| author_facet | Meyer, David Seis, Christian |
| contents | It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can be measured in terms of suitable Gagliardo seminorms. We propose a new approach to the study of regularity that is based on Littlewood-Paley theory, thus measuring regularity in terms of Besov norms. We recover the results that are available in the literature and extend these optimally to the diffusive setting. As a consequence, we derive sharp bounds on rates of convergence in the zero-diffusivity limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10860 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Propagation of regularity for transport equations. A Littlewood-Paley approach Meyer, David Seis, Christian Analysis of PDEs It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can be measured in terms of suitable Gagliardo seminorms. We propose a new approach to the study of regularity that is based on Littlewood-Paley theory, thus measuring regularity in terms of Besov norms. We recover the results that are available in the literature and extend these optimally to the diffusive setting. As a consequence, we derive sharp bounds on rates of convergence in the zero-diffusivity limit. |
| title | Propagation of regularity for transport equations. A Littlewood-Paley approach |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2203.10860 |