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EnglishThe purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of the Dirac equation with rough potentials. We focus in particular on bounded perturbations, arising as the Weyl quantization of suitable time-dependent symbols, as well as on quadratic and sub-quadratic non-smooth functions, hence generalizing the results in [40]. We then prove local well-posedness on the same function spaces for the nonlinear Dirac equation with a general nonlinearity, including power-type terms and the Thirring model. For this study we adopt the unifying framework of vector-valued time-frequency analysis [56]; most of the preliminary results are stated under general assumptions and hence they may be of independent interest.
Time-frequency analysis of the Dirac equation / Trapasso, S. I.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 269:3(2020), pp. 2477-2502.
| Titolo: | Time-frequency analysis of the Dirac equation |
| Autori: | |
| Data di pubblicazione: | 2020 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jde.2020.02.002 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| trapasso dirac tfa.pdf | 2. Post-print / Author's Accepted Manuscript |  | Embargo: 05/02/2022 Richiedi una copia | |
| 1-s2.0-S0022039620300577-main.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
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