The nonlinear dynamics of charged-surface instability development was
investigated for liquid helium far above the critical point. It is found that,
if the surface charge completely screens the field above the surface, the
equations of three-dimensional (3D) potential motion of a fluid are reduced to
the well-known equations describing the 3D Laplacian growth process. The
integrability of these equations in 2D geometry allows the analytic description
of the free-surface evolution up to the formation of cuspidal singularities at
the surface.Comment: latex, 5 pages, no figure
