【廿周年院庆学术报告18】· 【和山数学论坛第324期】
一、报告题目：Global existence of smooth solutions to 2D axisymmetric Euler equations with large initial data
二、报告人：赖耕副教授
三、时间：2022年9月24日(周六) 下午 15:00-16:00
四、腾讯会议号：232-362-665
报告摘要：We study the Cauchy problem of two-dimensional (2D) compressible Euler equations with axial symmetry. Although there has been much progress on the global existence of entropy solutions for the 2D axisymmetric Euler equations, much less is known about the global existence of smooth solutions. In this paper we find some sufficient conditions on the initial data to ensure the global existence of bounded smooth solutions in the whole space. The main difficulty for the global existence is to establish a priori $C^1$-norm estimates for the solutions. To this end, we derive several groups of suitable characteristic decompositions for the 2D axisymmetric Euler equations. Owing to the good structure of these characteristic decompositions, we construct some invariant regions for the derivatives of the sound speed. Using these invariant regions we establish a priori $C^1$-norm estimates for the solutions. The method introduced here should be also used to construct global smooth solutions for some other multi-dimensional hyperbolic conservation laws with symmetry. This is a joint work with Z.J. Yuan
报告人简介：赖耕，上海大学副教授，博士毕业于上海大学数学系，随后在复旦大学从事博士后工作，主持国家自然科学基金项目两项，曾合作获得上海市自然科学二等奖。主要从事非线性双曲守恒律方程组的研究，特别是对可压Euler方程组的二维Riemann问题、气体动力学中的激波反射问题、气体向真空扩散问题、超声速射流问题的研究，目前已在Arch. Ration. Mech. Anal.、J. Math. Pures Appl.、SIAM J. Appl. Math.、SIAM J. Math. Anal.、Indiana Univ. Math. J.等著名数学期刊上发表学术论文多篇。
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