Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	苏一鸣副教授,浙江工业大学
Inviter:
Title:	Construction of multi-bubble blow-up solutions to the $L^2$-critical half-wave equation
Language:	Chinese
Time & Venue:	2023.12.15 11:00-12:00 腾讯会议：695-437-096
Abstract:	We study the bubbling phenomena for the $L^2$-critical half-wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow-up solutions concentrating exactly at these singularities. This provides the first examples of multi-bubble solutions for the half-wave equation. In particular, the solutions exhibit the mass quantization property.Unlike the single-bubble or NLS cases, different bubbles exhibit the strongest interactions for the $L^2$-critical half-wave equation in dimension one. We find that there exists a narrow room between the orders $\|t\|^{2+}$ and $\|t\|^{3-}$ for the remainder in the geometrical decomposition. Based on this, a novel bootstrap scheme is introduced to address the multi-bubble non-local structure. The talk is based on a joint work with Cao Daomin and Zhang Deng.