# UBC Mathematics Colloquium

## Tai-Peng Tsai

(UBC)

## Navier-Stokes flows with scaling invariant bounds

### Fri., Oct. 9, 2009, 3:00pm, MATX 1100

The three dimensional incompressible Navier-Stokes system has two
different structures: The antisymmetry of the nonlinearity, which
provides an a priori bound for L^2 norm, and its natural scaling, which
preserves L^3 norm. After a brief survey, I will talk about two
problems. First the regularity problem, with a focus on current results
assuming scaling invariant bounds (Type I singularity). Second the
asymptotics problem, both temporal and spatial.