Speaker: Shijun Zheng (Georgia Southern University)

Title: Semilinear Schroedinger Equation with Magnetic Potentials


In quantum physics the magnetic Schroedinger equation provides an ideal and robust model when a Bose-Einstein Condensate is confined or released. As we will understand, the attractive or repulsive property of the potential has implications in geometry as well as in physics. We will present the analytic approach to show the existence of the solution within its lifespan. The techniques from Harmonic Analysis include Strichartz and smoothing estimates, Besov and Sobolev embeddings for a magnetic perturbation, and, bilinear estimates for fractional derivatives. Some intimate connection with the heat kernel estimates will also be discussed.