Abstract: Regularity criteria for weak solution of the electro-hydrodynamics was studied. It was proved that the solution (u,n,p,Ψ) remains strong on [0,T] if u∈L^s(0,T;L^r,∞(Ω)) or ‖u‖_{Ls,∞(0,T;Lr,∞(Ω))}≤C, where (3/r)+(2/s)=1 and r∈(3,∞], C>0 depending only on r and Ω.

Key words: electro-hydrodynamics, regularity criteria, weak solution, strong solution, weak L^p functions