# Frank Merle

## Université de Cergy-Pontoise & IHES

### On the implosion of a three dimensional compressible fluid

We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity.