Estimation time of existence water waves

R.V. Shamin

P.P. Shirshov Institute of Oceanology of the Russian Academy of Sciences,

Moscow, Russia

Equations describing nonstationary flow of ideal fluid with a 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 estimating the lifetime of solutions for such equations are developed and justified. An example of numerical calculation by these methods is given.

This work was supported by the Russian Foundation for Basic Research (grants 07-01- 00268-a and 07-05-00648-a) and INTAS Ref. Nr 05-1000008-8014