Title: Weak-strong uniqueness in fluid dynamics,
Abstract: We give a survey of recent results on weak-strong uniqueness for compressible
and incompressible Euler and Navier-Stokes equations, and also make some new
observations. The importance of the weak-strong uniqueness principle stems, on
the one hand, from the instances of non-uniqueness for the Euler equations
exhibited in the past years; and on the other hand from the question of
convergence of singular limits, for which weak-strong uniqueness represents an
elegant tool.