Systematic search for extreme and singular behaviour in some fundamental models of fluid mechanics

This review article offers a survey of the research program focused on a systematic computational search for extreme and potentially singular behaviour in hydrodynamic models motivated by open questions concerning the possibility of a finite-time blow-up in the solutions of the Navier-Stokes system. Inspired by the seminal work of Lu & Doering (2008 Ind. Univ. Math. 57, 2693-2727), we sought such extreme behaviour by solving PDE optimization …