Abstract: In this work we study the nonlocal transport equation derived recently by Steinerberger [Proc. Amer. Math. Soc., 147(11):4733{4744, 2019]. When this equation is considered on the real line, it describes how the distribution of roots of a polynomial behaves under iterated dierentiation of the function. This equation can also be seen as a nonlocal fast diusion equation. 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 et al. [Adv. Math., 194(1):203{223, 2005].

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