Academic Report of School of Mathematical Sciences [2026] No. 023

(Series Report for High-Level University Construction No. 1282)

Title：Critical scattering for the NLS on waveguide manifold

Speaker：Yongming Luo, Associate Professor (Beijing Institute of Technology–Moscow)

Time：10:00-11:00, Apr. 2, 2026

Location：Room 1420, Huiwen Building

Abstract：We consider the small data scattering in critical space of the NLS on waveguide manifold. Our work is mainly inspired by a recent paper of Kwak and Kwon, where the well-posedness of the periodic NLS in full mass-supercritical regime of any spatial dimension is settled. In the waveguide setting, we encounter the major challenge that the classical Strichartz estimates initiated by Hani and Pausader are no longer available in high-dimensional waveguides. We overcome such difficulty by developing an anisotropic generalization of the framework by Kwak and Kwon, where we also take certain novel interpolation techniques within Besov spaces into account. By doing so, we settle the small data scattering problem for the NLS on waveguide manifold in the full mass-supercritical regime of any spatial dimension.

Speaker Profile：Yongming Luo  is currently an associate professor in the Department of Computational Mathematics and Control at Beijing Institute of Technology–Moscow University in Shenzhen. His primary research focus is the long-time asymptotic behavior of scattering equations, and he has published numerous research papers in academic journals such as the Journal of Functional Analysis (JFA), Mathematical Annals (Math. Ann.), and the Journal of Geometric Analysis (J. Geom. Anal.).

Faculty and students are welcome to attend!

Invited by: He Mei

School of Mathematical Sciences

March 31, 2026