Mathematical foundations

on nonlinear dispersive waves

by Dr L. Ridgway Scott

Departments of Computer Science and Mathematics, University of Chicago

Syllabus

(1) Fundamental background in water flow and surface waves

  • Navier-Stokes equations
  • Free-surface problems
  • Non-Newtonian flows.

(2) History and basic models in 1-D

  • Relation to tsunamis
  • Properties of models
  • Comparison of models

(3) Numerical schemes

  • Early attempts
  • Changing the model
  • State of the art

(4) Models in 3-D

  • Model derivation-basic properties
  • Relation to Euler equations(vortex¬†blob)
  • Stability results

(5) Recent results

  • Numerical methods: state of the art
  • Comparison of models