Cauchy problem

Weak solutions of the 2D Euler equations

Stefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, Italy

Feb 11, 15:00 - 16:00

B1 L3 R3119

Cauchy problem Euler equations

In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.