On the Prandtl's Boundary Layer Theory for Steady Sink-Type Flows

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:2023-11-27 09:45





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.