Phase space analysis of higher-order dispersive equations with point interactions
Analysis of PDEs
2024-07-23 v1 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
Abstract
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.
Cite
@article{arxiv.2407.15521,
title = {Phase space analysis of higher-order dispersive equations with point interactions},
author = {Sonia Mazzucchi and Fabio Nicola and S. Ivan Trapasso},
journal= {arXiv preprint arXiv:2407.15521},
year = {2024}
}
Comments
19 pages