On the estimate of lifetime for solutions of the Cauchy–Kovalevskaya system with examples in hydrodynamics of ideal fluid with free surface

Equations describing nonstationary flow of ideal fluid with free surface are considered. They are investigated in conformal variables. For such equations, the correct solvability is proved in a scale of spaces of analytic functions. Constructive methods of estimation of lifetime of solutions for such equations are developed and justified. An example of numerical calculation by these methods is given.