There was some activity a while ago, like 10 years ago, string theoreists try to relate
- the fluid dynamics, for example, governed by Navier-Stokes equation,
- the Einstein gravity, and its relations to holography (such as AdS/CFT),
Naively, it looks that the development there is just trying to relate one problem to the other problem. For example, explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. See for example, studied in
and References therein. There is also a Breakthrough Prize in Fundamental Physics awarded to the developement of this direction.
My question is that have these efforts from "string theory and Einstein gravity" also affected the mathemtical study of Navier-Stokes equation and fluid dynamics? What are new progresses? What are new and solid lessons have we learned in mathemtics of Navier-Stokes equation and fluid dynamics then after this development? (i.e. the impacts on the community of mathemticians.)
Thanks for the References/answers!