勷勤数学•杰出学者报告

题      目：On the Prandtl’s theory for steady sink Type

报  告  人：辛周平  教授  (邀请人：李进开)

                                 香港中文大学

时      间：11月11日  16：10-17：10

地     点：数科院西楼111报告厅

报告人简介:

         辛周平，国际数学家大会45分钟报告人，教育部长江讲座教授，曾获得世界华人数学家大会最高奖--“晨兴数学金奖”，现任香港中文大学蒙民伟数学讲座教授、数学科学研究所常务所长。辛教授是偏微分方程的理论分析、数值计算及其应用，和非线性波、数学物理、流体力学等领域的著名专家，在线性和非线性波的渐近稳定性、粘性消失极限、边界层理论、高维激波理论、松弛格式和涡点方法和高维Navier-Stokes方程等方面做出了许多原创性的实质贡献。担任《Methods Appl. Anal.》主编、《J. Math. Phys.》、《Math. Models Methods Appl. Sci.》副主编，担任《Sci. China Math.》和《Math. Models Methods Appl. Sci.》在内的等十多个重要学术期刊的编委。

摘      要：

       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.

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