On a nonlocal differential equation describing roots of polynomials under differentiation
Analysis of PDEs
2018-12-04 v1 Dynamical Systems
Abstract
In this work we study the nonlocal transport equation derived recently by Steinerberger when studying how the distribution of roots of a polynomial behaves under iterated differentation of the function. In particular, we study the well-posedness of the equation, establish some qualitative properties of the solution and give conditions ensuring the global existence of both weak and strong solutions. Finally, we present a link between the equation obtained by Steinerberger and a one-dimensional model of the surface quasi-geostrophic equation used by Chae, C\'ordoba, C\'ordoba and Fontelos.
Keywords
Cite
@article{arxiv.1812.00082,
title = {On a nonlocal differential equation describing roots of polynomials under differentiation},
author = {Rafael Granero-Belinchón},
journal= {arXiv preprint arXiv:1812.00082},
year = {2018}
}