# mp.mathematical physics – Fluid dynamics of Navier-Stokes, Einstein's gravity and holography

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,

to

• 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

"From Navier-Stokes to Einstein" 10.1007 / JHEP07 (2012) 146 – by
Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger

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!