Partial Differential Equations and Applied Mathematics Seminar
Date/Time: March, 9th, Thur., 4:00 ~ 5:00 PM
Location: cmac seminar room
Speaker: Younghun Hong
Affiliation: cmac,Yonsei University
Title: The optimal convergence rate for non-relativistic limits and existence of a stationary solution to the pseudo-relativistic nonlinear Schro\"dinger equation.
We construct a radially symmetric stationary solution to the pseudo-relativistic nonlinear Schr\"odinger equation (including some super-critical range of nonlinearities) via a "simple" contaction mapping argument, which is completely non-variational. As a by-product, we obtain the optimal rate of convergence to the non-relativistic ground state as the speed of light c goes to infinity. In our approach, non-degeneracy of the ground state of the limit equation plays a crucial role, but it also seems that non-degeneracy is the only necessary thing we should have. Thus, our method can be adapted very easily to other physical settings. This talk is based on a joint work with Woocheol Choi and Jinmyoung Seok.