EVENT DETAILS AND ABSTRACT

Title: Almost conservation laws and global wellposedness
Speaker: Professor James Colliander
Speaker Info: Berkeley
Brief Description:
Special Note:
Abstract:

A dynamical reinterpretation of the $L^2$ mass conservation law for solutions of the $KdV$ equation has led to a general procedure for proving {\it{almost conservation laws}} for solutions of nonlinear Hamiltonian PDE. The almost conserved quantities have been used to globalize the available local-in-time wellposedness results for various $KdV$ and $NLS$ type equations and will provide insights into the long-time behavior of solutions. This talk will survey the known local theory, highlighting aspects requiring further investigation. The procedure for constructing almost conserved quantities will be described.