Title: The I-method and its application.
Speaker: Debdeep Bhattacharya
Date and Time: Friday, October 27 , 3:00-4:00pm
Place: Rome 206
Abstract: Developed by Colliander-Keel- Staffilani-Takaoka-Tao in 2001, the so called "I-method" has been extensively used to prove the global well-posedness of various nonlinear dispersive equations for data with infinite energy, where the classical energy-conservation arguments fail. The method uses a modified energy functional which is "almost conserved" in time, leading to a global existence. Following the work of Farah-Linares-Pastor we shall demonstrate this method for the geralized KdV equation and outline an improvement of available global well-posedness results for the modified Zakharov-Kuznetsov equation in 2D