The Second Iterate of the Muskat Equation in Supercritical Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908732073443328 |
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| author | Paduro, Esteban |
| author_facet | Paduro, Esteban |
| contents | The ill-posedness for the Muskat problem in spaces that are supercritical with respect to the scaling is studied. The main result of the paper establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard's iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04694 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Second Iterate of the Muskat Equation in Supercritical Spaces Paduro, Esteban Analysis of PDEs 76S05, 76B03, 35Q35, 35B30 The ill-posedness for the Muskat problem in spaces that are supercritical with respect to the scaling is studied. The main result of the paper establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard's iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space. |
| title | The Second Iterate of the Muskat Equation in Supercritical Spaces |
| topic | Analysis of PDEs 76S05, 76B03, 35Q35, 35B30 |
| url | https://arxiv.org/abs/2209.04694 |