Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids (Q2898367)

The authors introduce an intrinsic definition of suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids, and establish its existence for any finite-energy initial data. The definition is independent of existence of hypothetical solutions and adaptable to various classes of domains and boundary conditions. In addition, the solutions satisfy the relative entropy inequality and enjoy the weak-strong uniqueness property discussed in [\textit{P. Germain}, ``Weak-strong uniqueness for the isentropic compressible Navier-Stokes system'', J. Math. Fluid Mech. 13, No. 1, 137--146 (2011; \url{doi:10.1007/s00021-009-0006-1})]. Last, an explicit construction of suitable weak solutions by means of a family of approximate problems is provided.