The fundamental progresses achieved in recent years by the mathematical theory of hyperbolic conservation laws and fluid dynamics (classical and non classical) have opened the dam to a whole host of further advances both in theoretical aspects and in the applications, as well as in new research trends originating by surprising and deep connections of the field of nonlinear hyperbolic PDEs with other branches of analysis. The topics of these achievements include: mixing of incompressible fluids and well-posedness of transport equation for nearly incompressible vector fields; convex integration for Euler equation and Magnetohydrodynamics; energy equality for the Navier-Stokes equations; stability/instability of shear flows for the hydrostatic Euler equations; transport of vortex points/sheets in fluids; singular limits for fluid dynamics models; surface waves on the plasma-vacuum interface; compactness, regularity, Lagrangian representation of solutions of hyperbolic conservation laws, possibly in presence of local or non-local source term; well-posedness of conservation laws in granular flow models.

The school will be a forum that brings together world leading experts in these subjects, junior researchers and PHD students, with the aim to discuss different methodologies and approaches to address problems originating in the above research themes. The workshop comprises two courses and a series of plenary lectures held by internationally renowned speakers. It will also host the assignment of the Gold Medal in honour of Guido Stampacchia awarded by the Italian Mathematical Union together with the Ettore Majorana Foundation to a young mathematician (whose age be not greater than 35) for his scientific contribution in the field of Calculus of Variation and applications.