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On a nonlocal differential equation describing roots of polynomials under differentiation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2020Embargo end date: 01 Jan 2018 Spain Publisher:International Press of BostonJournal:Communications in Mathematical Sciences, volume 18, pages 1,643-1,660 (issn: 1539-6746, eissn: 1945-0796,

Authors: Rafael Granero-Belinch n; Rafael Granero-Belinchón;

doi: 10.4310/cms.2020.v18.n6.a6 , 10.48550/arxiv.1812.00082

arXiv: http://arxiv.org/abs/1812.00082

handle: 10902/29548

On a nonlocal differential equation describing roots of polynomials under differentiation

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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��rdoba, C��rdoba and Fontelos.

Country

Spain

Related Organizations

University of Cantabria
Spain

Keywords

Mathematics - Analysis of PDEs, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Analysis of PDEs (math.AP)

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