On exact solutions of the equation of continuity

The continuum of exact solutions of the two-dimensional continuity equation for stationary, planeparallel fluid flow is found in the article. Only specific solutions of this equation corresponding to a vortex-free fluid flow are described in the classical literature. At the same time, components of an arbitrary analytical function of a complex variable are used, playing the role of a velocity potential and a current function. In this paper we give a generalization of this method, which also gives vortex-free solutions to the continuity equation.