Some time ago there was some activity, like 10 years ago, string theorists try to relate
- the fluid dynamics, for example, governed by Navier-Stokes equation,
- the Gravity of einstein, and its relationships with holography (such as AdS / CFT),
Naively, it seems that the development there is just trying to relate one problem to the other problem. For example, explicit construction that for each solution of the Navier-Stokes equation incompressible in $ p + 1 $ dimensions, there is a "dual" solution uniquely associated with the Einstein equations of vacuum in $ p + 2 $ dimensions. See for example, studied in
and References in it. There is also an Advances Prize in Fundamental Physics awarded to the development of this address.
My question is: have these efforts of "Einstein's string theory and gravity" also been affected in the mathematical study of the Navier-Stokes equation and the dynamics of fluids? What are the new developments? What new and solid lessons have we learned in mathematics from the Navier-Stokes equation and fluid dynamics after this development? (for example, for the mathematical community).
Thanks for the references / answers!