Developable surfaces as generators of the ``isobaric solutions'' to the Euler equations (Q1773113)

The authors seek solutions to Euler equations for which the pressure vanishes identically. It is shown that the general solutions of this problem can be obtained in terms of Cartesian pieces of developable surfaces \(x_3=F(x_1,x_2)\) with vanishing Gaussian curvature. At that, the initial condition for velocity field is a clockwise \(\pi/2\) rotation of gradient \(F(x_1,x_2)\). The proof is based on the study of eigenvalues of the Jacobian matrix of initial velocity.