Dynamics for the Fractional Nonlinear Schrodinger Equation

PDE Seminar
Tuesday, August 25, 2015 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Department of Mathematics, Sichuan Normal University
In this talk, we consider the dynamical properties of solutions to the fractional nonlinear Schrodinger equation (FNLS, for short) arising from pseudorelativistic Boson stars. First, by establishing the profile decomposition of bounded sequences in H^s, we find the best constant of a Gagliardo-Nirenberg type inequality. Then, we obtain the stability and instability of standing waves for (FNLS) by the profile decomposition. Finally, we investigate the dynamical properties of blow-up solutions for (FNLS), including sharp threshold mass, concentration and limiting profile. (Joint joint with Jian Zhang)