## Finite time singularity of the Euler-Poincare equation

### Xinwei Yu

Alberta

We consider the Euler-Poincare equation in $\mathbb{R}^d$ with $d\ge 2$. For a large class
of smooth initial data we prove that the corresponding solution blows up in finite time. Our
analysis exhibits some new concentration mechanism and hidden monotonicity formula
associated with the Euler-Poincare flow. No size restrictions are imposed on the data.
We also showcase a class of initial data for which the corresponding solution exists globally
in time. This is joint work with Dong Li and Zhichun Zhai.