蔡東和Dong-Ho Tsai

中國立清華大學數學系教授

投入數學及流體力學 鑽研幾何曲率流有成

My current research direction is mostly academic, related to mathematics and some area of fluid mechanics. During the past 5 years, my research interest is mainly on the geometric evolution ( also known as curvature flow ) of a given convex closed plane curve, which is in the category of initial value problem for a 2x2 system of nonlinear parabolic partial differential equation. The purpose is t o study the long time behavior of the e volution and to investigate whether it has a smooth convergence or has a formation of singularity during the evolution. The success of the investigation relies on some good estimates on the solutions of v arious important equations and on the c ontrol of the g eometry of the e volving curve. Until no w, I hav e worked on many diff erent types of int eresting cur vature flows (both local and nonlocal ) and obtained rather detailed and complete results. One of my recent important research results is to give a theoretical proof that it is possible to have an n-fold symmetric curve as the limiting shape of a nonlocal curvature flow ( which has a prescribed rate of change in the enclosed area and is motivated by the well-known Hele-Shaw flow problem ) , where the initial data is an arbitrary convex closed curve in the plane. This result is new in the literature and appeared in the journal with wide circulation: “SIAM Journal of Mathematical Analysis, 2018 ＂.

得獎感言

　I would like to express my sincere and grateful thanks to MOST for this outstanding research award. It gives recognition on my past effort and research results and also gives me a gr eat deal of enc ouragement and support t o continue my r esearch in the futur e.

個人勵志銘

“Logic will g et you from A t o Z; imagina tion will g et you everywhere.＂ ( Albert Einstein )