In April, Dr. Quoc-Hung Nguyen, an assistant professor at the Institute of Mathematical Sciences at ShanghaiTech, has had a research article entitled “Quantitative Estimates for Regular Lagrangian Flows with BV Vector Fields” released online in Communications on Pure and Applied Mathematics (CPAM)，one of the most prestigious mathematics journals in the world. The journal was established in 1948 by Courant Institute of Mathematical Sciences. Its very first volume included articles on Boltzmann Transport Equation that is also among the topics Dr. Nguyen treats in the current work.
The article, marking the culmination of 18 months’ intensive work, studies regular Lagrangian flows with BV vector fields, a research direction that has been actively pursued in the last two decades and has proven to be fruitful. Dr. Nguyen proves in this paper the well-posedness of the flow and quantitative stability. His proof combines a host of new ideas and tools, including a creative use of Kakeya singular operator, never used before in this context.
“The ideas and techniques introduced in this work will certainly have long-lasting impact on the study of ordinary differential equations and transport equations with non-smooth coefficients”, said Prof. Xiuxiong Chen, the Founding Director of IMS and an expert in partial differential equations. “Hung brings a collection of insights into the current research that has allowed him to make important contributions to our understanding of many fundamental questions.”
Dr. Nguyen came to ShanghaiTech in the Fall of 2019, following a postdoctoral position at NYU Abu Dahbi. In the seven years since the completion of his doctoral studies, he has published over 40 research articles many of which have appeared in prestigious journals including JFA, JMPA, JEMS, Comm. PDE, Archive, Potential Analysis, CMP, and Annals of PDE. He is the organizer of a well-attended online PDE seminar which counts among its invited speakers many of the leading experts in the field including Fields medalists. “IMS always supports and encourages me to do high-level research”, Dr. Nguyen said recently. “The environment of the institute has greatly influenced my research in the last two years.”