题目：On uniqueness of multi-bubble blow-up solutions and multi-solitons to L^2-critical NLS

报告人：苏一鸣（浙江工业大学）

时间：3月23日星期四下午4:00-5:00

地点：五教5406

摘要：We are concerned with the focusing L^2-critical nonlinear Schrodinger equations. The uniqueness is proved 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+}. Moreover, we also prove the uniqueness in the energy class of multi-solitons which converge to a sum of K solitary waves with convergence rate (1/t)^{2+}. The uniqueness class is further enlarged to contain the multi-solitons with even lower convergence rate (1/t)^{1/2+} in the pseudo-conformal space. The proof is mainly based on several upgradation procedures of the convergence of remainder in the geometrical decomposition, in which the key ingredients are several monotone functionals constructed particularly in the multi-bubble case.