Global Well-posedness of a coupled KdV system of Majda and Biello.
- Rio de Janeiro: IMPA, 2014.
- video online
The Fourth Workshop on Fluids and PDE was held at the National Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, Brazil, from Monday 26 May to Friday 30 May 2014. This workshop is held every two to three years in Brazil. The fourth edition of the workshop was the closing event of a Thematic Program on Incompressible Fluids Dynamics, to be held at IMPA next Spring. Hence, the focus of the workshop will be incompressible fluid mechanics .
We study a coupled KdV system, introduced by Majda and Biello, describing nonlinear resonant interaction of Rossby waves. We show the global well-posedness of this system with periodic boundary condition in L2. Our approach is based on a successive time-averaging method developed by Babin, Ilyin and Titi (2011) on classic KdV equation. This is a joint work with K. Simon and E. S. Titi .