Globally Well-Posed Shallow-Water Equations

                             by 

                   David Levermore ( U. of AZ, Math)


             JTB 120, 3:20pm  Friday, February 20, 1998


                          Abstract

An introduction will be given to the ``lake'' and ``great lake''
equations.  These equations arise to leading and first order in a
small aspect ratio expansion of a low Froude number (i.e.\ low wave
speed) and very small wave amplitude limit of the three dimensional
incompressible Euler equations in a basin with a free upper surface
and a spatially varying bottom topography.  Gravity waves are thereby
removed from the models while currents are retained.  The resulting
equations conserve energy and convect a potential vorticity.  These
properties are used to show these models are well-posed in weak,
classical and analytic classes, and moreover, that the solution
depends continuously on the bottom topography.  These results allow
for a rigorous justifcation of the small aspect ratio expansion.


Requests for preprints and reprints to: lvrmr@math.arizona.edu
This source can be found at http://www.math.utah.edu/applied-math/