If the 3D incompressible NS equation will blowup in finite time is one of the most important problems in mathematics. Since the well-known results by Leray in 1934, there was a lot of progress on this problem by theoretical studies. Even though, the final answer to this problem seems still extremely far away.
On the other side, a lot of studies on scientific computing was searching for solutions with possible finite time singularity, aiming on some clues to the PDE analysis. The candidates include the Taylor-Green flow, the anti-parallel vortex tubes, and the Kida-Pelz setup with high symmetry. The work on scientific computing ranges from proposing new candidates, ruling out possibilities of finite time blowups, and revealing flow structures with vorticity growth. These studies may contribute not only new clues to theoretical studies, but also new methods to improve the capcity and performance of scientific computing itself.
Following this route, in this talk I will introduce some progress of scientific computing in searching for the finite time singularity of 3D incomrepssible Euler and NS equations.