Event Date
2012-02-20
Event Time
02:30 pm ~ 03:20 pm
Event Location
Wachman 617
Abstract: I will consider the focusing NLS equation in one, two and three space dimensions with different powers of nonlinearities (including cubic and quintic powers) and their global solutions with finite energy $H^{1}$ initial data. My discussion will focus on blow up solutions and known types of their dynamics. In particular, I will show that the class of so-called ‘log-log’ blow up solutions can blow up not only on a single point set but on various geometric sets such as circles, spheres, cylinders, while remaining regular (in the energy space) away from the blow-up core.