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In this paper our goal is to define a renormalised dissipativemeasure--valued (rDMV) solution of compressible Navier--Stokes system forfluids with non-monotone pressure--density relation. We prove existence of rDMVsolutions and establish a suitable relative energy inequality. Moreover weobtain the Weak (Measure-valued)-Strong uniqueness property of this rDMVsolution with the help of relative energy inequality.

On weak (measure-valued)-strong uniqueness for compressible Navier-Stokes system with non-monotone pressure law