Speaker：Zhouping Xin (The Chinese University of Hong Kong)

Time：2023-11-27, 9:45

Location：Conference Room 106 at Experiment Building at Haiyun Campus

Abstract:

In this talk, I will present some results on the large Reynolds number limits and asymptotic behaviors of solutions to the steady incompressible Navier-Stokes equations in two-dimensional infinitely long convergent nozzles, The main results show that the Prandtl’s laminar boundary layer theory can be rigorously established and the sink-type Euler flow superposed with a self-similar Prandtl’s boundary layer flow is shown to be uniformly structurally stable as long as the viscous flow has a given negative mass flux and the boundaries of the nozzle satisfy a curvature decreasing condition. Furthermore, the asymptotic behaviors of the solutions at both the vertex and infinity can be determined uniquely which plays a key role in the stability analysis. Some of key ideas in the theory will be discussed. This talk is based on a joint work with Dr. Chen Gao.