Gravitational principle of minimum pressure for incompressible flows

We consider the flows of ideal (Euler equations) and Newtonian viscous (Navier–Stokes equations) incompressible fluids in the gravitational field of mass forces. In this case, the gravitational field created by the liquid itself (self-gravity) is also taken into account. It is shown that some well-known principles of maximum pressure, according to which either the pressure is constant in the flow region, or the minimum pressure is reached at the boundary of this region if the forces of self-gravity are taken into account, exclude the case of constant pressure. It is also demonstrated that self-gravity makes it impossible for waves and solitons to pass with pressure minima to the surface of a body flown around by a viscous fluid.