Several different transport processes, such as heat transport, momentum transport and charge transport, may take place at the same time in the quark-gluon plasma (QGP). The corresponding transport coefficients are heat conductivity, shear viscosity and electric conductivity respectively. In the present paper, we will study the color-electric conductivity of the QGP in presence of shear viscosity, which is focused on the connection between the charge transport and the momentum transport. To achieve that goal, we solve the viscous chromohydrodynamic equations which are obtained from the QGP kinetic theory associated with the distribution function modified by shear viscosity. According to the solved color fluctuations of hydrodynamic quantities we obtain the induced color current through which the color-electric conductivity is derived. Then we study viscous effects on the color-electric conductivity. In the viscous chromohydrodynamic approach, the conductivity properties of the QGP are mainly demonstrated by the longitudinal part of the color-electric conductivity. Shear viscosity has an appreciable impact on real and imaginary parts of the color-electric conductivity in some frequency region.
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