About the compressible-incompressible limit

In this talk, we will discuss two methods (a global one and a local one), developped in collaboration with P.L.Lions, to handle the compressible-incompressible limit when the Mach number goes to zero. The difficulty comes from the pesence of high oscillations in time (acoustic waves). We will also give some application to the case of vanishing viscosities and also to the Boltzmann equation.