On Kato's smoothing effects for KdV and Benjamin type equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917544028274688 |
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| author | Garzón, Carlos Riaño, Oscar |
| author_facet | Garzón, Carlos Riaño, Oscar |
| contents | We analyze how the interaction between local and nonlocal dispersions, combined with different types of nonlinearities, influences the smoothing effects of solutions. To achieve this goal, we consider a model that generalizes the KdV and Benjamin equations and demonstrate that its solutions exhibit Kato's smoothing effect and satisfy the propagation of regularity principle. As a result, we confirm that the higher-order dispersive term determines the local gain of fractional regularity of solutions. Our results are general; they not only recover known results for the KdV and Benjamin equations, but also provide new insights for a broader family of models of physical and mathematical interest with polynomial dispersions of arbitrary order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Kato's smoothing effects for KdV and Benjamin type equations Garzón, Carlos Riaño, Oscar Analysis of PDEs 35Q35, 35Q53, 35B05, 35B60 We analyze how the interaction between local and nonlocal dispersions, combined with different types of nonlinearities, influences the smoothing effects of solutions. To achieve this goal, we consider a model that generalizes the KdV and Benjamin equations and demonstrate that its solutions exhibit Kato's smoothing effect and satisfy the propagation of regularity principle. As a result, we confirm that the higher-order dispersive term determines the local gain of fractional regularity of solutions. Our results are general; they not only recover known results for the KdV and Benjamin equations, but also provide new insights for a broader family of models of physical and mathematical interest with polynomial dispersions of arbitrary order. |
| title | On Kato's smoothing effects for KdV and Benjamin type equations |
| topic | Analysis of PDEs 35Q35, 35Q53, 35B05, 35B60 |
| url | https://arxiv.org/abs/2605.30009 |