报告题目：Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

报告专家：黄飞敏（中国科学院华罗庚首席研究员、博士生导师）

报告时间：2019年6月14日16:00-17:30

报告地点：东校区8教406

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摘要：We establish the existence and uniqueness of compressible or incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheet or entropy wave. We develop a new method to show the existence without assumptions of the sign of the second order derivatives on the velocity, or on the Bernoulli functions and the 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 sheet or Entropy wave by the compensated compactness. It is the first result on the global existence of solutions of the multi-dimensional steady compressible full Euler equations with free boundaries, which is not a perturbation of a piecewise constant solution. Finally, via the incompressible limit, we also establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solution with vortex sheet. The methods and techniques developed in this paper may have applications in other related problems.

专家简介：黄飞敏，博士，教授、博士生导师，中科院华罗庚首席研究员。曾获2013年国家自然科学奖二等奖，国家杰出青年基金获得者，获2004年美国工业与应用数学协会杰出论文奖。主要从事非线性偏微分方程的研究工作。