Further a priori estimates in Gas Dynamics through Compensated Integrability

In recent times, we elaborated a tool, called Compensated Integrability, which provides Strichartz-like inequalities for some systems of conservation laws. We were able to derive space-time estimates for Gas dynamics, in terms of internal variables like pressure and density. We shall describe new developments, in particular a multilinear version of C.I., and derive additional estimates. These involve either the velocity field, or singular integrals.