Abstract : The compressible Euler equation with physical vacuum is a free boundary problem in gas dynamics, where the moving boundary represents the interface between gas and vacuum states, with the density decaying to zero at the boundary. Such problems have been traditionally studied using a Lagrangian approach and at high regularity. In this work we propose a comprehensive alternative approach, fully within the Eulerian setting, and which leads to sharp results. This is joint work with Marcelo Disconzi and Mihaela Ifrim.