Abstract
AbstractUp to now, we have imposed very general restrictions concerning the constitutive relations characterizing the material properties of the fluid. In particular, the piece of information that can be deduced from the energy and entropy balance was not sufficient to obtain an unconditional result of the weak–strong uniqueness property without the extra assumptions concerning boundedness of the density and the temperature. In this chapter, we fix the hypotheses imposed on the equation of state as well as the transport coefficients and establish a general weak–strong uniqueness principle valid in the class of finite energy weak solutions. The same set of hypotheses will guarantee the existence of global in time weak solutions for any finite energy/entropy initial data.
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