Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes system in dimension d ≥ 3. We use new a priori estimates, which enable us to deal with low-regularity data and vanishing density. In particular, we prove new well-posedness results which improve the results of Danchin 6] by considering a less regular initial density, without a lower bound. Also, we obtain the first uniqueness criterion for weak solutions which is at the scaling of the equation.