Weak-strong uniqueness property for the full Navier-Stokes-Fourier   system
  The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions. 
Eduard Feireisl and Antonin Novotny
math.AP