# Analysis and Mathematical Physics

## Duality of Fluid Mechanics and Solution of Decaying Turbulence

I will describe the duality of incompressible Navier-Stokes fluid dynamics in three dimensions, leading to its reformulation in terms of a one-dimensional momentum loop equation.

The decaying turbulence is a solution of this equation equivalent to a string theory with discrete target space made of regular star polygons and Ising degrees of freedom on the sides.

This string theory is solvable in the turbulent limit, equivalent to the quasiclassical approximation in a nontrivial calculable background.

As a result, the spectrum of decay indexes is analytically computed, and it agrees very well with real and numerical experiments.

Among the decay indexes there are complex conjugate pairs related to zeros of the Riemann zeta function. The Kolmogorov scaling laws are refuted.

The momentum loop equation does not have finite-time blow-up solutions.