Solvability of a class of evolution operators on compact Lie groups
Analysis of PDEs
2026-02-18 v1
Abstract
This paper provides sufficient conditions for the solvability of a class of first-order evolution operators of Vekua-type on the product of a one-dimensional torus and a compact Lie group. The conditions are expressed in terms of the time-dependent coefficients and the spectral behavior of a normalized left-invariant vector field on the group. The three-sphere case is discussed in detail, leading to more explicit criteria, and the main results are further extended to operators defined on finite products of compact Lie groups.
Cite
@article{arxiv.2602.15203,
title = {Solvability of a class of evolution operators on compact Lie groups},
author = {Alexandre Kirilov and Wagner Augusto Almeida de Moraes and Pedro Meyer Tokoro},
journal= {arXiv preprint arXiv:2602.15203},
year = {2026}
}
Comments
17 pages