Uniqueness for active scalar equations in a Zygmund space

Article type: Research Article

Authors: Cozzi, Elaine^{; *}

Affiliations: Department of Mathematics, Oregon State University, USA. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider a class of active scalar equations which includes, for example, the 2D Euler equations, the 2D Navier–Stokes equations, and various aggregation equations including the Keller–Segel model. For this class of equations, we establish uniqueness of solutions in the Zygmund space C∗0. This result improves upon that in (Trans. Amer. Math. Soc. 367 (2015) 3095–3118), where the authors show uniqueness of solutions in BMO. As a corollary of our methods, we establish the uniform in space vanishing viscosity limit of Hölder continuous solutions to the aggregation equation with Newtonian potential.

Keywords: Active scalars, inviscid limit

DOI: 10.3233/ASY-221762

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 531-551, 2022