Weak-Strong Uniqueness in Fluid Dynamics

Various concepts of weak solution have been suggested for the fundamental equations of inviscid fluid flow over the last few decades. A common problem is the vast degree of non-uniqueness that all these types of solution exhibit. Nevertheless, a conditional notion of uniqueness, the so-called weak-strong uniqueness, can be established in various situations. We present some recent results, both positive and negative, on weak-strong uniqueness in the realm of incompressible and compressible fluid dynamics.