Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918322321227776 |
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| author | Schippa, Robert Tataru, Daniel |
| author_facet | Schippa, Robert Tataru, Daniel |
| contents | The goal of this paper is to prove bilinear $L^p$ estimates for rough dispersive evolutions satisfying non-degeneracy and transversality assumptions. The estimates generalize the sharp Fourier extension estimates for the cone and the paraboloid. To this end, we require a wave packet decomposition with localization properties in space-time and space-time frequencies. Secondly, we construct a refined wave packet parametrix for dispersive equations with $C^{1,1}$-coefficients by using the FBI transform. As a consequence, we obtain bilinear estimates for solutions to dispersive equations with $C^{1,1}$ coefficients provided that the solutions interact transversely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows Schippa, Robert Tataru, Daniel Analysis of PDEs The goal of this paper is to prove bilinear $L^p$ estimates for rough dispersive evolutions satisfying non-degeneracy and transversality assumptions. The estimates generalize the sharp Fourier extension estimates for the cone and the paraboloid. To this end, we require a wave packet decomposition with localization properties in space-time and space-time frequencies. Secondly, we construct a refined wave packet parametrix for dispersive equations with $C^{1,1}$-coefficients by using the FBI transform. As a consequence, we obtain bilinear estimates for solutions to dispersive equations with $C^{1,1}$ coefficients provided that the solutions interact transversely. |
| title | Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.23551 |