This analysis reveals the existence of unique dissipative measure-valued solutions for compressible fluids, indicating their alignment with classical solutions.
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.
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Yang et al. (2025) studied this question.
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