Phase space analysis of higher-order dispersive equations with point interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911963969224704 |
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| author | Mazzucchi, Sonia Nicola, Fabio Trapasso, S. Ivan |
| author_facet | Mazzucchi, Sonia Nicola, Fabio Trapasso, S. Ivan |
| contents | We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets) of the corresponding fundamental solution - in fact, locating the modulation/amalgam space regularity of such generalized Fresnel-type oscillatory functions is a problem of independent interest in harmonic analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase space analysis of higher-order dispersive equations with point interactions Mazzucchi, Sonia Nicola, Fabio Trapasso, S. Ivan Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis 35Q55, 35J10, 42B15, 35B30, 35Q40, 42B35 We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets) of the corresponding fundamental solution - in fact, locating the modulation/amalgam space regularity of such generalized Fresnel-type oscillatory functions is a problem of independent interest in harmonic analysis. |
| title | Phase space analysis of higher-order dispersive equations with point interactions |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis 35Q55, 35J10, 42B15, 35B30, 35Q40, 42B35 |
| url | https://arxiv.org/abs/2407.15521 |