报告摘要：

       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. We first review the numerical evidence of finite time singularity for 3D axisymmetric Euler equations by Luo and Hou. The singularity is a ring like singularity that occurs at a stagnation point in the symmetry plane located at the boundary of the cylinder. We then present a novel method of analysis and prove finite time singularity of the 2D Boussinesq and 3D Euler equations with C^{1,\alpha} initial velocity and boundary, whose solutions share some essential features similar to those reported in the Luo-Hou computation.

Finally, we present some recent numerical results on singularity formation of the 3D axisymmetric Navier-Stokes equations with degenerate diffusion coefficients.

嘉宾简介：

       侯一钊，美国加州理工学院应用数学系Charles Lee Powell教授，美国艺术与科学院院士。主要研究领域为应用数学和计算数学，在流体力学、多尺度问题、非线性偏微分方程等方面取得了许多原创性科研成果。先后获Sloan Fellowship，冯康科学计算奖，美国物理学会Francois N.Frenkiel奖，工业与应用数学学会(SIAM)James H.Wilkinson计算数学奖，美国计算力学学会计算与应用科学奖，华人数学家大会晨兴应用数学金奖。曾应邀在1998年国际数学家大会作特邀报告和2003年国际工业与应用数学大会作大会报告。