Speaker: Professor Yuan Baoquan
Topic: Global regularity for the 2D micropolar Rayleigh-B\'{e}nard convection system with velocity zero dissipation and temperature critical dissipation
Date: July 3, 2023
Time: 10:00 - 11:00 a.m.
Venue: Academic Lecture Hall 1506, Building 9
Sponsors: School of Mathematics and Statistics, Research Institute of Mathematical Science, Institute of Science and Technology
Biography：
Yuan Baoquan is a professor, doctor and doctoral supervisor. He is the leader of the Mathematics Key Discipline and a high-level talent in Henan Province. He serves as the Executive Director of the Henan Mathematical Society and has received the Henan Provincial Outstanding Young Scientist Fund. He is also recognized as an academic and technical leader by Henan Education Department and is a key young and middle-aged teacher in Henan Province. He has conducted research visits to various research institutions, including the Courant Institute of Mathematical Sciences at New York University, the Department of Mathematics at Oklahoma State University, the Institute of Mathematical Research at The Chinese University of Hong Kong and the Institute of Applied Physics and Computational Mathematics in Beijing. His research focuses on partial differential equations and partial differential equations in mathematical fluid dynamics. He has led and completed six projects funded by the National Natural Science Foundation of China, including three general programs. He has published more than 70 papers in domestic and international academic journals such as Science China, Acta Mathematica Sinica, JDE, and SIAM JMA.
Abstract:
In this talk I will talk on the global regularity problem for the 2D micropolar Rayleigh-B\'{e}nard convection system with velocity zero dissipation, micro-rotation velocity Laplace dissipation and temperature critical dissipation. By introducing a combined quantity and using the technique of Littlewood-Paley decomposition, we will establish the global regularity result of solutions to this system.
Our result shows that, for the Euler-Rayleigh-B\'{e}nard convection system, the temperature critical dissipation can guarantee the global regularity of solutions in the 2 dimensional case.