On the theory of Maxwell liquids. II

The classical local solvability of the periodic boundary-value problem and Cauchy problem for the system
\begin{gather} \frac{dv}{dt}+v_k\frac{\partial v}{\partial x_k}-\Delta u+\operatorname{grad} p=f_1,\;v=\nu_1u+\nu_2\frac{\partial u}{\partial t},\;\operatorname{div} v=0,\;\nu_1, \nu_2>0, \end{gather}
is proved. The system (1) describes motions of Maxwell liquids.