题目：Soliton resolution for Calogero--Moser derivative nonlinear Schrödinger equation

报告人：Soonsik Kwon (Korea Advanced Institute of Science and Technology(KAIST))

时间：6月17日上午10:00-11:00

地点：五教5307

摘要：I will present a soliton resolution result for the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by Gérard and Lenzmann, who demonstrated its Lax pair structure. Additionally, (CM-DNLS) exhibits several symmetries, such as mass-criticality with pseudo-conformal symmetry and a self-dual Hamiltonian. Despite its integrability, finite-time blow-up solutions have been constructed.

We establish soliton resolution for both finite-time blow-up solutions and global solutions in a fully general setting, \emph{without imposing radial symmetry or size constraints}. A key aspect of our proof is the control of the energy of the outer radiation after extracting a soliton, referred to as the \emph{energy bubbling} estimate. This benefits from two levels of conservation laws, mass and energy, and self-duality. This approach allows us to directly prove continuous-in-time soliton resolution, bypassing time-sequential soliton resolution. Importantly, our proof does not rely on the integrability of the equation, potentially offering insights applicable to other non-integrable models. This is a joint work with Taegyu Kim.