Global well-posedness for some cubic dispersive equations

PDE Seminar
Tuesday, March 24, 2015 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
Johns Hopkins University
In this talk we examine the cubic nonlinear wave and Schrodinger equations. In three dimensions, each of these equations is H^{1/2} critical. It has been showed that such equations are well-posed and scattering when the H^{1/2} norm is bounded, however, there is no known quantity that controls the H^{1/2} norm. In this talk we use the I-method to prove global well posedness for data in H^{s}, s > 1/2.