Dynamics of ideal liquid with free surface in conformal variables

Problems of the mathematical hydrodynamics with free surface in conformal variables are studied. Analytical solvability in Hilbert space scale and numerical techniques of finding approximate solutions are considered. Lifetime for solutions, a constructive evaluation, and an application of mathematical statistics to the solvability of nonlinear equations are studied. Multiple numerical experiments of the methods considered are shown. A lot of these methods can be applied not only to problems of the mathematical hydrodynamics with a free surface, but to abstract Cauchy–Kovalevskaya problems in Banach spaces scales as well.