报告人：王天怡副教授（武汉理工大学）
时 间：2019年9月22日上午 11:00-11:45
地点：华南数学应用与交叉研究中心学术报告厅111
题目：On Steady Euler Flows with Large Vorticity and Characteristic Discontinuities
摘要：
In this talk, we want to present the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. A new approach is introduced for the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by the compensated compactness argument. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, the existence and uniqueness of incompressible Euler flows is established in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solution with vortex sheets. This is the joint work with Gui-Qiang G. Chen, Fei-Min Huang, and Wei Xiang.
个人简介：
王天怡，2014年毕业于中国科学院数学与系统科学研究院，现任职于武汉理工大学理学院。公开发表SCI论文多篇，部分研究结果发表在本领域国际顶尖学术期刊 ：《Advances in Mathematics》、《Archive for Rational Mechanics and Analysis》，研究结果被SCI 期刊他引31次，专著引用2次。受邀在中国数学会2017年学术年会、HYP (Hyperbolic Problems Theory, Numerics, Applications)，以及英国牛津大学、英国巴斯大学、美国乔治亚理工学院、意大利萨索科学研究中心、香港中文大学等单位作了相关学术报告。主持国家自然科学基金项目2项。