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 Uspekhi Mat. Nauk, 2007, Volume 62, Issue 3(375), Pages 95–116 (Mi umn6759)

Mathematical aspects of surface water waves

W. Craiga, C. E. Wayneb

a McMaster University
b Boston University, Department of Mathematics and Statistics

Abstract: The theory of the motion of a free surface over a body of water is a fascinating subject, with a long history in both applied and pure mathematical research, and with a continuing relevance to the enterprises of mankind having to do with the sea. Despite the recent advances in the field (some of which we will hear about during this Workshop on Mathematical Hydrodynamics at the Steklov Institute), and the current focus of the mathematical community on the topic, many fundamental mathematical questions remain. These have to do with the evolution of surface water waves, their approximation by model equations and by computer simulations, the detailed dynamics of wave interactions, such as would produce rogue waves in an open ocean, and the theory (partially probabilistic) of approximating wave fields over large regions by averaged ‘macroscopic’ quantities which satisfy essentially kinetic equations of motion. In this note we would like to point out open problems and some of the directions of current research in the field. We believe that the introduction of new analytical techniques and novel points of view will play an important rôle in the future development of the area.

DOI: https://doi.org/10.4213/rm6759

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English version:
Russian Mathematical Surveys, 2007, 62:3, 453–473

Bibliographic databases:

UDC: 517.958+531.32
MSC: Primary 76B15; Secondary 35Q53, 35Q55

Citation: W. Craig, C. E. Wayne, “Mathematical aspects of surface water waves”, Uspekhi Mat. Nauk, 62:3(375) (2007), 95–116; Russian Math. Surveys, 62:3 (2007), 453–473

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/umn6759
• https://doi.org/10.4213/rm6759
• http://mi.mathnet.ru/eng/umn/v62/i3/p95

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