On pressureless Euler equation with external force (Q6629736)

The authors consider some Hodograph equations for the \(n\)-dimensional Euler equations with the constant pressure and external force. They demonstrate that solutions of the multidimensional equation have a remarkable novel property which does not exist in one dimensional case. Namely, they show that in the even dimensions for external force the solutions of the Equation are periodic in time with certain period T. Moreover, they show some particular examples in one, two and three dimensions, including the case of Coriolis external force.