Academic Report
Title: The global smooth solution of the 3D incompressible Euler and Navier-Stokes equations in spherical coordinates
Reporter: Prof. WANG Shu (Beijing University of Technology)
Time: Sept 27, 2019 (Friday) AM 10:00-11:00
Location: A1101# room, Innovation Park Building
Contact: Prof. LI Fengquan (tel:15164005929)
Abstract: We investigates the globally stabilizing effects of the geometry of the domain and the solution in studying the regularity issue on the three-dimensional incompressible avier-Stokes and Euler system. We establish the global existence and uniqueness of the smooth solution to the Cauchy problem for the three-dimensional incompressible Navier-Stokes and Euler system, and, also, to the initial boundary value problem for the 3D Navier-Stokes equations, in spherical oordinates for a class of the smooth large initial data. This is the first result on the global existence and uniqueness of the smooth solution to the 3D incompressible Navier-Stokes and Euler quations in spherical coordinates. The related problems the axisymmetric Navier-Stokes equations are surveyed and some results on the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations will also be reviewed.
The brief introduction to the reporter: Wang Shu, Ph.D., Professor, doctoral supervisor, now professor of Beijing University of technology and distinguished professor of Guangzhou University's hundred talents program, professor in charge of the doctoral degree authorization point of the first level discipline of mathematics of Beijing University of technology, director of the "Applied Mathematics" discipline of Beijing key construction discipline, director of China's industrial and applied mathematics Council, state Experts on the evaluation of meetings of the Overseas Study Fund Committee and the National Natural Science Foundation of China. He was a member of the Chinese Mathematics Association and Dean of the School of Applied Mathematics and Science of Beijing University of Technology. In 2001, he was elected as an outstanding postdoctoral candidate of the Chinese Academy of Sciences, in 2004, the Ministry of Education in the new century, in 2008, Beijing, Beijing, China, Beijing University of Technology, and Beijing Great Wall Scholars in 2012. In 2016, he received special allowances from the State Council Government. He graduated from Henan University in 1990, Beijing University of Technology in 1993 and Nanjing University in 1998. He has worked as a postdoctoral fellow at the Institute of Mathematics, the University of Vienna, Austria, a senior visiting scholar at California Institute of Technology, and a visiting professor at Blaise Pascal University, France, Germany, Italy, Austria, Japan, Czech Republic, Singapore and Hong Kong. Over 20 times, the district has conducted academic exchanges, cooperation and visits. He has presided over or presided over eight projects of the National Natural Science Foundation of China (including one key project), won one second prize of Beijing Science and Technology Award independently, and published three books. He has published more than 100 SCI academic papers in Adv. In Math., ARMA, SIAM J Math Anal, CPDE, J. Diff. Eqns and other magazines.
