This talk pertains to a well-posedness result for inhomogeneous incompressible Euler system in Besov spaces framework.

We will first give an overview about the classical (homogeneous) case. Then we will state our claims and explain the main ideas of the proof. In doing this, we will also introduce the basic tools, from Fourier Analysis, we used to achieve our results: Littlewood-Paley decomposition and paradifferential calculus.

This is a joined work with R. Danchin.