Weak-strong uniqueness in fluid dynamics. (English) Zbl 1408.35158

Wiedemann, Emil

Fefferman, Charles L. (ed.) et al., Partial differential equations in fluid mechanics. Based on the workshop “PDEs in Fluid Mechanics”, Warwick, UK, September 26–30, 2016. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 452, 289-326 (2018).

Summary: 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.
For the entire collection see [Zbl 1398.35004].

MSC:

35Q35	PDEs in connection with fluid mechanics
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35B35	Stability in context of PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

weak-strong uniqueness; compressible and incompressible Euler and Navier-Stokes equations; well-posedness