  Recent years have seen spectacular progress in the mathematical study of
hydrodynamic equations. Novel tools from convex integration in particular prove
extremely versatile in establishing non-uniqueness results. Motivated by this
'pathological' behavior of solutions in the deterministic setting, stochastic
models of fluid dynamics have enjoyed growing interest from the mathematical
community. Inspired by the theory of 'regularization by noise', it is hoped for
that stochasticity might help avoid 'pathologies' such as non-uniqueness of
weak solutions. Current research however shows that convex integration methods
can prevail even in spite of random perturbations.
