Low regularity well-posedness for the generalized surface quasi-geostrophic front equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913030356336640 |
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| author | Ai, Albert Avadanei, Ovidiu-Neculai |
| author_facet | Ai, Albert Avadanei, Ovidiu-Neculai |
| contents | We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us to prove the local well-posedness of the non-periodic gSQG front equation at a low level of regularity (in the SQG case, at only one-half derivatives above scaling). In addition, we establish global well-posedness for small and localized rough initial data, as well as modified scattering, by using the testing by wave packet approach of Ifrim-Tataru. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07551 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Low regularity well-posedness for the generalized surface quasi-geostrophic front equation Ai, Albert Avadanei, Ovidiu-Neculai Analysis of PDEs 35Q35, 35B65 We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us to prove the local well-posedness of the non-periodic gSQG front equation at a low level of regularity (in the SQG case, at only one-half derivatives above scaling). In addition, we establish global well-posedness for small and localized rough initial data, as well as modified scattering, by using the testing by wave packet approach of Ifrim-Tataru. |
| title | Low regularity well-posedness for the generalized surface quasi-geostrophic front equation |
| topic | Analysis of PDEs 35Q35, 35B65 |
| url | https://arxiv.org/abs/2311.07551 |