Journal of Mathematical Sciences

, Volume 160, Issue 5, pp 537–678 | Cite as

Dynamics of an ideal liquid with a free surface in conformal variables

  • R. V. Shamin


Problems of mathematical hydrodynamics with a free surface in conformal variables are studied. Analytical solvability in Hilbert space scale and numerical techniques of finding approximate solutions are considered. The lifetime for solutions, a constructive evaluation, and 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 mathematical hydrodynamics with a free surface but to abstract Cauchy–Kovalevskaya problems in Banach spaces scale as well.


Free Surface Surface Wave Machine Accuracy Taylor Instability Abstract Cauchy Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Shirshov Institute of Oceanology of the Russian Academy of Sciences Laboratory of nonlinear processesMoscowRussia

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