Keywords: Fluid dynamics, Integrable systems, Conservation Laws, Hamiltonian Mechanics, PDEs singularities.

"The efforts of a child trying to dam a small stream flowing in the street and his surprise at the strange way the water works its way out has its analog in our attempts over the years to understand the flow of fluids. We have tried to dam the water up — in our understanding — by getting the laws and the equations that describe the flow. [...] we will describe the unique way in which water has broken through the dam and escaped our attempts to understand it." R. P. Feynman (1963)

The previous sentence has not lost its relevance even in regards to the modern understanding of fluid physics. Many classical experimental aspects, such as turbulence or the characterization of singularities, do not have satisfactory theoretical modeling. On the more mathematical side, the very existence of solutions to the Navier-Stokes equation for any time remains unknown.

My research area concerns fluids in 2 and 3 spatial dimensions with particular attention to interface motions in oceanic and atmospheric models.

I also study nonlinear wave models close to integrability, from which toextract qualitative information on the formation of singularities in finite times and on their structure.

• Math. Dept.

• Milano B.