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Journal Articles
Trapasso, S. Ivan
Time-frequency analysis of the Dirac equation Journal Article
In: J. Differential Equations, vol. 269, no. 3, pp. 2477–2502, 2020.
Abstract | Links | BibTeX | Tags: Dirac equation, modulation spaces, partial differential equations, pseudodifferential operators, time-frequency analysis
@article{T_JDE_20,
title = {Time-frequency analysis of the Dirac equation},
author = {S. Ivan Trapasso},
url = {https://arxiv.org/abs/1909.09842, arXiv
https://www.sciencedirect.com/science/article/pii/S0022039620300577/pdfft?md5=9529d30135284078192dbd0cbc114288&pid=1-s2.0-S0022039620300577-main.pdf, PDF},
doi = {10.1016/j.jde.2020.02.002},
year = {2020},
date = {2020-07-15},
urldate = {2020-07-15},
journal = {J. Differential Equations},
volume = {269},
number = {3},
pages = {2477–2502},
publisher = {Academic Press},
abstract = {The 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 a recent paper by Kato and Naumkin. 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 as developed by Wahlberg; most of the preliminary results are stated under general assumptions and hence they may be of independent interest.},
keywords = {Dirac equation, modulation spaces, partial differential equations, pseudodifferential operators, time-frequency analysis},
pubstate = {published},
tppubtype = {article}
}
The 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 a recent paper by Kato and Naumkin. 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 as developed by Wahlberg; most of the preliminary results are stated under general assumptions and hence they may be of independent interest.