Dissipative Measure‐Valued Solutions of the Compressible Navier–Stokes–Korteweg System

ABSTRACT This work rigorously demonstrates the global‐in‐time existence of dissipative measure‐valued solutions for the Navier–Stokes–Korteweg system describing compressible viscous fluids with intrinsic capillarity effects on periodic spatial domains. Furthermore, we prove a weak–strong uniqueness principle that such dissipative measure‐valued solutions coincide with classical solutions when both emanate from identical initial data.