School of Mathematical Sciences Academic Report [2025] 051  

(High-Level University Construction Series Report No. 1073)  

Date & Time: January 24, 2025, 1:30 PM – 5:30 PM  

Venue: Room 514, Convergence Stars Building, Yuehai Campus, Shenzhen University  

Lecture 1 Title: Cubic Dirac equations with a class of large data  

Time: 1:30 PM – 2:20 PM  

Speaker: Asst. Prof. Shijie Dong (Southern University of Science and Technology)  

Abstract: We are interested in massless cubic Dirac equations in two and three space dimensions, known as the Soler model. We aim to show global existence and asymptotic behaviour for this model with a class of large initial data. This is joint with Kuijie Li and Jingya Zhao.

Biography: Shijie Dong, Assistant Professor at SUSTech, received his B.S. from Ocean University of China (2014), M.S. from Yonsei University (2017), and Ph.D. from Sorbonne Université (LJLL Laboratory, 2019). After postdoctoral research at Fudan University (2020–2022), he specializes in nonlinear hyperbolic PDEs and general relativity, publishing in Comm. Math. Phys., JFA, and SIMA.  

Lecture 2 Title: Inviscid limit of Navier-Stokes equations with vortex patch data  

Time: 2:20 PM – 3:10 PM  

Speaker: Assoc. Prof. Jingchi Huang (Sun Yat-sen University)  

Abstract: We justify the zero-viscosity limit for Navier-Stokes equations in a half-space with L^\infty initial vorticity using vorticity formulation and conormal derivatives. Energy methods establish this limit for analytic data.  

Biography: Jingchi Huang, Associate Professor at SYSU, obtained his Ph.D. from AMSS-CAS and conducted postdoctoral research at Penn State. Focusing on Navier-Stokes equations, his work appears in ARMA, JFA, JMPA, and DCDS. He leads multiple NSFC projects.  

Lecture 3 Title: Nonlinear Stability of Rarefaction Wave to the One-Dimensional Quantum-Navier-Stokes Equations  

Time: 3:30 PM – 4:20 PM  

Speaker: Prof. Mingjie Li (Minzu University of China)  

Abstract: We prove time-asymptotic stability for weak rarefaction waves in 1D Quantum-Navier-Stokes equations with small initial perturbations via L^2-energy methods and L^p-decay estimates for smoothed waves.  

Biography: Mingjie Li, Professor and Master’s Supervisor at Minzu University, publishes in Arch. Ration. Mech. Anal. and SIAM J. Math. Anal. Leading NSFC Youth/General Programs, he was selected for MUC’s High-Level (2016–2019) and Outstanding Youth (2019–2022) Talent Programs.  

Lecture 4 Title: Nonlinear Stability of 2D Steady Water Waves  

Time: 4:20 PM – 5:10 PM  

Speaker: Assoc. Res. Prof. Qingtang Su (Morningside Center of Mathematics, AMSS)  

Abstract: While almost global well-posedness under smooth localized perturbations was established by Wu, Ionescu-Pusateri, and Alazard-Delort, nonlinear stability remained open. We resolve this longstanding problem for 2D steady water waves.  

Biography: Qingtang Su, Associate Researcher at AMSS, earned his Ph.D. from University of Michigan. His work on water waves—covering well-posedness, stability, and instability—includes the first rigorous proof of Stokes wave’s nonlinear modulation instability (discovered 1967). Published in Ann. PDE, CMP, and ARMA.  

All faculty and students are welcome!  

Invited by: Prof. Qingtian Zhang  

School of Mathematical Sciences  

January 24, 2025