Lecture by Prof. Boqing Dong from Shenzhen University
time: 2017-06-12

Title:Global well-posedness and large-time decay for the 2D micropolar flows

Time: Wed, Jun.14, 2017, AM 10:30-11:50

Speaker: Prof. Boqing Dong (Shenzhen University)

Location:Room 4318, Building No.4, Wushan Campus

Abstract: 

   In this talk, we will investigate the global (in time) regularity and large time behavior of solutions to the 2D micropolar flows with only angular viscosity dissipation. Micropolar flows model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium.When there is no kinematic viscosity in the momentum equation,the global regularity problem is not easy due to the lack of suitable bounds on the derivatives.The idea here is to fully exploit the structure of the system and control the vorticity via the evolution equation of a combined quantity of the vorticity and the micro-rotation angular velocity. To understand the large time behavior, we overcome two main difficulties,the lack of kinematic viscosity and the presence of linear terms.  We introduce a diagonalization process to eliminate the linear terms and rely on the uniform bounds for the first derivatives of the solutions to generate suitable decay rates.