Series: Mathematics Colloquium

Date: Thursday, April 18, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Diane Henderson

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Walter Craig, McMaster University

Title: On Solitary Water Waves

Abstract: 

In the subject of free surface water waves, the solitary waves play an
important role in the theory of two dimensional fluid motions.  These
are steady solutions to the Euler equations which are localized,
positively elevated above the mean fluid level, and traveling at
velocities with supercritical Froude number, they provide a stable
mechanism in bodies of water for transport of mass, momentum and
energy over long distances.  In this talk I will explain that in the
three (or higher) dimensional problem of surface water waves, there do
not exist any localized, steady positive solutions to the Euler
equations.  Additionally I will present some recent results of
A.-M. Matei and myself on the local a priori regularity of free
surface flows, with and without the presence of surface tension.