Uniqueness of Weak Solutions to an Electrohydrodynamics Model

Abstract

This paper studies uniqueness of weak solutions to an electrohydrodynamics model in ${\mathrm{\backslash Bbb\; R}}^d\left(d=2,3\right)$. When $d=2$, we prove a uniqueness without any condition on the velocity. For $d=3$, we prove a weak-strong uniqueness result with a condition on the vorticity in the homogeneous Besov space.