[01789] On uniqueness of multi-bubble blow-up solutions and multi-solitons to L^2-critical NLS
Session Time & Room : 3C (Aug.23, 13:20-15:00) @G709
Type : Contributed Talk
Abstract : This talk is concerned with the long-time behavior of solutions to the focusing $L^2$-critical nonlinear Schrodinger equations. Firstly, we briefly review the existence and uniqueness of multi-bubble blow-up solutions and multi-solitons in the context of NLS. Then, we introduce the uniqueness for a large energy class of multi-bubble blow-up solutions, which converge to a sum of $K$ pseudo-conformal blow-up solutions particularly with the low rate $(T-t)^{0+}$. Lastly, we also discuss the uniqueness of multi-solitons which converge to a sum of $K$ solitary waves with convergence rate $(1/t)^{2+}$ in the energy space, and with even lower convergence rate $(1/t)^{1/2+}$ in the pseudo-conformal space. The talk is based on the joint work with Prof. Daomin Cao and Prof. Deng Zhang, which has been published in "Archive for Rational Mechanics and Analysis" in 2023.
