Low regularity well-posedness for KP-I equations: the dispersion-generalized case
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916090266779648 |
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| author | Sanwal, Akansha Schippa, Robert |
| author_facet | Sanwal, Akansha Schippa, Robert |
| contents | We prove new well-posedness results for dispersion-generalized Kadomtsev--Petviashvili I equations in $\mathbb{R}^2$, which family links the classical KP-I equation with the fifth order KP-I equation. For strong enough dispersion, we show global well-posedness in $L^2(\mathbb{R}^2)$. To this end, we combine resonance and transversality considerations with Strichartz estimates and a nonlinear Loomis--Whitney inequality. Moreover, we prove that for small dispersion, the equations cannot be solved via Picard iteration. In this case, we use an additional frequency dependent time localization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_02037 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Low regularity well-posedness for KP-I equations: the dispersion-generalized case Sanwal, Akansha Schippa, Robert Analysis of PDEs 35Q35, 35Q53 We prove new well-posedness results for dispersion-generalized Kadomtsev--Petviashvili I equations in $\mathbb{R}^2$, which family links the classical KP-I equation with the fifth order KP-I equation. For strong enough dispersion, we show global well-posedness in $L^2(\mathbb{R}^2)$. To this end, we combine resonance and transversality considerations with Strichartz estimates and a nonlinear Loomis--Whitney inequality. Moreover, we prove that for small dispersion, the equations cannot be solved via Picard iteration. In this case, we use an additional frequency dependent time localization. |
| title | Low regularity well-posedness for KP-I equations: the dispersion-generalized case |
| topic | Analysis of PDEs 35Q35, 35Q53 |
| url | https://arxiv.org/abs/2205.02037 |