Bernoulli law under minimal smoothness assumptions (Q656255)

In the present paper the author generalizes the Bernoulli law under the minimal smoothness assumption on both the domain as well as weak solution. Assuming that, e.g., the computational domain is simply connected and that the velocity and pressure are (weak) solutions of the stationary incompressible Euler equations, then for every subset of the computational domain the following holds: if the streamlines are constant then the head pressure stays constant almost everywhere in the corresponding subset. This results follows from the previous theoretical works of the author and his co-authors on the Morse-Sad property and level sets of Sobolev spaces and BV spaces.