In search of local singularities in ideal potential flows with free surface

Understand

For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data.

• This is so despite great advances over the last 25 years in the mathematical analysis of the Euler equations for water waves.
• Here we expand our earlier work (Chin.
• Ann.