# Notes on INS (19): Thomas Hou’s papers

See the latest papers in the following list:

http://www.acm.caltech.edu/~hou/#2

and also the slides of the talks by Hou (2010):

www.math.duke.edu/conferences/FAN2010/Talks/Talk_Duke_Hou.pdf

www.ima.umn.edu/2009-2010/W2.22-26.10/activities/Hou-Thomas/Talk_IMA_Hou.pdf

(print them out & read them, compare with the work by Seregin etc.)

Some excerpts from Hou’s slides & papers:

(Beale-Kato-Majda criterion, 1984) $u$ ceases to be classical at $T$ if  and only if $\int_0^T \|\omega\|_{\infty}(t) dt = \infty$, where $\omega$ is the vorticity field.

In 1993 (and 2005), R. Kerr [Phys. Fluids] presented numerical evidence of 3D Euler singularity for two anti-parallel vortex tubes.  Kerr’s initial condition was considered as “the most attractive candidate for potential singular behavior” of the 3D Euler equations.(Majda and Bertozzi, “Vorticity and Incompressible Flow”, 2002)

Pelz’s filament model indeed leads to a finite time blowup [PRE, 97]. But when we use the same high symmetry initial condition to solve
the full 3D Euler equations, the solution remains regular.

[Numerical simulation] 256 parallel processors with maximal memory comsumption 120Gb. The laregest number of grid points is close to 5 billions.

… the convection term contributes to stability [by canceling out other nonlinear term]…

… a 3D modification of INS admits a finite-time blow-up (?).