Global mild solution for the Navier--Stokes--Nernst--Planck--Poisson system in Besov-weak-Herz spaces
• Aibo Liu,
• Jianing Xie
Aibo Liu
Liaoning Normal University
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Jianing Xie
Dongbei University of Finance and Economics
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## Abstract

We study a coupled Navier–Stokes–Nernst–Planck–Poisson system arising from electrohydrodynamics in critical Besov-weak-Herz spaces. When the initial value sufficiently small, we prove the existence and uniqueness of global mild solution to the cauchy problem in this spaces for $n\geq3$. The spaces is larger than some other known critical spaces.