  In fluid mechanics, a lot of authors have been reporting analytical solutions
of Euler and Navier-Stokes equations. But there is an essential deficiency of
non-stationary solutions indeed. In our presentation, we explore the case of
non-stationary flows of the Euler equations for incompressible fluids, which
should conserve the Bernoulli-function to be invariant for the aforementioned
system. We use previously suggested ansatz for solving of the system of
Navier-Stokes equations (which is proved to have the analytical way to present
its solution in case of conserving the Bernoulli-function to be invariant for
such the type of the flows). Conditions for the existence of exact solution of
the aforementioned type for the Euler equations are obtained. The restrictions
at choosing of the form of the 3D nonstationary solution for the given constant
Bernoulli-function B are considered. We should especially note that pressure
field should be calculated from the given constant Bernoulli-function B, if all
the components of velocity field are obtained.
