Title    name
2018 KAIX School in PDE
 
  Title
  Speaker Tatsuo Iguchi
  Date 2018-06-27
  Host
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.
 
Abstract : We consider the initial value problem to the Isobe-Kakinuma model for water waves.
As was shown by J. C. Luke, the water wave problem has a variational structure. By approximating the velocity potential in Luke's Lagrangian, we obtain an approximate La- grangian for water waves. The Isobe-Kakinuma model is a corresponding Euler-Lagrange equation for the approximate Lagrangian. In this talk, we rst explain a structure of the Isobe-Kakinuma model and then justify the model rigorously as a higher order shallow water approximation by giving an error estimate between the solutions of the model and of the full water wave problem. It is revealed that the Isobe-Kakinuma model is a much more precise model than the well-known Green-Naghdi equations.