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Exact solutions of a classical problem of a plane unsteady potential flow ofan ideal incompressible fluid with a free boundary are presented. The fluidoccupies a semi-infinite strip bounded by the free surface (from above) and(from the sides) by two solid vertical walls approaching each other with aconstant velocity. The solutions are obtained for a situation where thecapillary and gravity forces are absent, and the fluid motion is completelydetermined by the motion of the walls. The solutions contain an arbitraryfunction, which allows one to describe the nonlinear evolution of perturbationsof an arbitrary shape for an initially flat horizontal surface of the fluid.Examples of exact solutions corresponding to the formation of bubbles, cuspidalpoints, and droplets are considered.

Exact solutions of the problem of dynamics of a fluid with a free surface located between two approaching vertical walls