Global Existence for Nonlinear Dispersive Equation

Monday, February 2, 2009 -
4:00pm to 6:00pm
Starting from small data, when does a nonlinear dispersive PDE have global solutions? A classical approach, just like for ODE, is to study resonances. But I will show that for PDE a new kind of resonances arises, that I call space resonances. This is the basis of a new method, that I will present; I will also show how it applies to a variety of equations of Mathematical Physics: non-linear Schrödinger, water waves, Euler-Maxwell... This is joint work with Nader Masmoudi and Jalal Shatah.
Pierre Germain
Courant Institute for Mathematics, NYC
Event Location: 
Fine Hall 110