Compressible potential flows with free boundaries. I: Vibrocapillary equilibria (Q2722651)

The authors consider various variational formulations describing nonstationary compressible fluid flows with partially free boundaries in different exterior fields and under surface tension. The computation of the Hamilton action requires the solution of a time dependent family of Neumann problems for an elliptic equation. By transformation to nondiminsional variables and introduction of a small parameter characterizing the high-frequency contributions of the excitation, a class of oscillating solutions is constructed via truncating the Hamilton action. To get further information about the principal symbol and the mapping properties of the corresponding Jacobi operator the second variation of the potential is computed.