中山大学罗果博士作了题为三维轴对称欧拉方程的潜在奇异解的讲座，中山大学是直属的综合性重点大学，国家“985工程”、“211工程”建设高校，同时是“珠峰计划”、“111计划”、“卓越法律人才教育培养计划”、“卓越医生教育培养计划”实施高校。在职研究生讲座的主要内容是：

　　无论是3D不可压欧拉方程可以开发从光滑的初始数据在有限时间奇点是在数学流体力学中最具挑战性的问题之一。这项工作将尝试从一个数值来看，通过提供一类潜在的奇异解欧拉方程计算的轴对称的几何形状提供一个肯定的答案，这一长期悬而未决的问题。该解决方案满足在固体壁沿轴向的周期性边界条件和不流动边界条件。该公式使用混合6阶伽和6阶有限差分法，在专门设计的自适应(移动)网格的动态调整，以适应不断变化的解决方案离散空间。凭借超过(3 * 10 ^ 12)^ 2附近的奇异点的最大有效分辨率，我们能够提前解决高达tau_2 = 0.003505，预测t滑的奇点时～0.0035056，同时实现逐点相对于在涡度矢量和观测的最大涡一(3 * 10 ^ 8)倍增长 - 为O(4)10 ^()错误。数值数据进行比对所有主要的爆破(不爆破)的标准，其中包括比尔 - 加藤Majda，康斯坦丁 - Fefferman-Majda，邓侯宇，确认奇异的有效性。附近的奇异点当地的分析也表明自相似爆破的存在。我们还讨论一个1D模型可以被看作是一个本地近似圆柱体的固体边界附近的欧拉方程。这种一维模型的有限时间爆破证明一类的光滑初始数据，这基本上是在全3D爆破计算中使用的初始数据的限制。

　　罗果博士为中山大学学士，香港中文大学硕士，美国俄亥俄州立大学(Ohio State University)博士。毕业后在加州理工大学从事博士后研究，现在为香港城市大学数学系Assistant Professor。他的主要研究方向为偏微分方程的计算及理论。

　　原文：Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries. The solutions satisfy a periodic boundary condition along the axial direction and no-flow boundary condition on the solid wall. The equations are discretized in space using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially designed adaptive (moving) meshes that are dynamically adjusted to the evolving solutions. With a maximum effective resolution of over (3*10^12)^2 near the point of the singularity, we are able to advance the solution up to tau_2 = 0.003505 and predict a singularity time of t_s ~ 0.0035056, while achieving a pointwise relative error of O(10^(-4)) in the vorticity vector and observing a (3*10^8)-fold increase in the maximum vorticity. The numerical data is checked against all major blowup (non-blowup) criteria, including Beale-Kato-Majda, Constantin-Fefferman-Majda, and Deng-Hou-Yu, to confirm the validity of the singularity. A local analysis near the point of the singularity also suggests the existence of a self-similar blowup. We also discuss a 1D model which can be viewed as a local approximation to the Euler equations near the solid boundary of the cylinder. The finite-time blowup of this 1D model is proved for a class of smooth initial data, which are essentially restrictions of the initial data used in the full 3D blowup calculations.