On evolutionary equations related to skew-symmetric spatial operators
Analysis of PDEs
2025-04-24 v1
Abstract
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest a criteria of uniqueness of this semigroup. We also find a stronger criteria of uniqueness of generalized solutions. Applications to transport equations with solenoidal (and generally discontinuous) coefficients are given.
Cite
@article{arxiv.2504.16232,
title = {On evolutionary equations related to skew-symmetric spatial operators},
author = {Evgeny Yu. Panov},
journal= {arXiv preprint arXiv:2504.16232},
year = {2025}
}