Differential Equations and Applications Seminar
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Thu, 20/01/2005 16:30 |
Martin Vohralik (University Paris-Sud) |
Differential Equations and Applications Seminar  |
DH Common Room |
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Thu, 03/02/2005 16:30 |
Yuriy Semenov (National Academy of Science of Ukraine, Kiev) |
Differential Equations and Applications Seminar |
DH Common Room |
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Thu, 10/02/2005 16:30 |
Joseph D Fehribach (WPI The University of Science & Technology & Life (MA, USA)) |
Differential Equations and Applications Seminar |
DH Common Room |
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Thu, 17/02/2005 16:30 |
Apala Majumdar (University of Bristol) |
Differential Equations and Applications Seminar |
DH Common Room |
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Thu, 24/02/2005 16:30 |
Mike Cullen (Meteorological Office, UK) |
Differential Equations and Applications Seminar |
DH Common Room |
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Thu, 03/03/2005 16:30 |
Nim Arinaminpathy and John Fozard (OCIAM) |
Differential Equations and Applications Seminar |
DH Common Room |
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Thu, 10/03/2005 16:30 |
Mark Groves (Loughborough University) |
Differential Equations and Applications Seminar |
DH Common Room |
| The classical gravity-capillary water-wave problem is the study of the irrotational flow of a three-dimensional perfect fluid bounded below by a flat, rigid bottom and above by a free surface subject to the forces of gravity and surface tension. In this lecture I will present a survey of currently available existence theories for travelling-wave solutions of this problem, that is, waves which move in a specific direction with constant speed and without change of shape. The talk will focus upon wave motions which are truly three-dimensional, so that the free surface of the water exhibits a two-dimensional pattern, and upon solutions of the complete hydrodynamic equations for water waves rather than model equations. Specific examples include (a) doubly periodic surface waves; (b) wave patterns which have a single- or multi-pulse profile in one distinguished horizontal direction and are periodic in another; (c) so-called 'fully-localised solitary waves' consisting of a localised trough-like disturbance of the free surface which decays to zero in all horizontal directions. I will also sketch the mathematical techniques required to prove the existence of the above waves. The key is a formulation of the problem as a Hamiltonian system with infinitely many degrees of freedom together with an associated variational principle. | |||
